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Descubre los Logaritmos con Susi Profe: Ejercicios y Propiedades para 4 ESO y 1 Bachillerato

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_wywo

8/3/2023

Matemáticas I

Logaritmos: 1º Bachillerato

Asignaturas

/

Matemáticas I

/

Ecuaciones

/

Las ecuanciones exponenciales y logarítmicas

Descubre los Logaritmos con Susi Profe: Ejercicios y Propiedades para 4 ESO y 1 Bachillerato

Logarithms are mathematical tools used to solve exponential equations. They express the power to which a base number must be raised to obtain a given value. Logaritmos Susi Profe provides a comprehensive guide on logarithmic properties and applications, covering key concepts like:

  • Definition and notation of logarithms
  • Properties of logarithms
  • Solving logarithmic equations
  • Applying logarithmic properties to simplify expressions

Key points:
• Logarithms are the inverse operation of exponentiation
• The most common bases used are 10 (common logarithm) and e (natural logarithm)
• Understanding logarithmic properties is crucial for solving complex equations
• Practical applications include modeling exponential growth and decay

...

8/3/2023

1178

Logaritmos = Introducción los coqacimos nos ayudan • Log a Ei= Y= X → a* =y 2092 log decinae. logaritmo de un numero Y (positivo) en base a

Ver

Applying Logarithmic Properties

This page focuses on applying the properties of logarithms to solve various problems and simplify expressions. It provides several examples and exercises to reinforce understanding.

Example: Solve log_2(8/4) = x Solution: log_2(8/4) = log_2(8) - log_2(4) = 3 - 2 = 1

The page includes exercises on:

  • Evaluating logarithms with different bases
  • Simplifying logarithmic expressions using properties
  • Solving equations involving logarithms

Highlight: When solving logarithmic equations, it's crucial to ensure that the bases are the same before applying properties.

An important concept introduced is finding the base of a logarithm when given the logarithmic equation:

Example: Find the base b in the equation log_b(125) = 3 Solution: b^3 = 125, so b = 5

The page emphasizes the importance of practice in mastering logarithmic problem-solving techniques.

Logaritmos = Introducción los coqacimos nos ayudan • Log a Ei= Y= X → a* =y 2092 log decinae. logaritmo de un numero Y (positivo) en base a

Ver

Advanced Logarithmic Operations

This page delves into more complex logarithmic operations and problem-solving techniques. It covers the reduction and expansion of logarithmic expressions using various properties.

Example: Reduce log(x^3 * y^2) + 2log(√z) Solution: 3log(x) + 2log(y) + log(z^(1/2))

The page provides exercises on:

  • Combining logarithms with the same base
  • Expanding logarithms of products and quotients
  • Simplifying complex logarithmic expressions

Highlight: When reducing or expanding logarithmic expressions, always ensure that the properties are applied correctly and consistently.

An important technique introduced is the use of change of base formula:

log_a(x) = log_b(x) / log_b(a)

This formula allows for the conversion between logarithms of different bases, which is particularly useful when dealing with calculators that only compute natural or common logarithms.

Vocabulary: The change of base formula is a fundamental tool in logarithmic problem-solving, especially for logaritmos neperianos (natural logarithms).

Logaritmos = Introducción los coqacimos nos ayudan • Log a Ei= Y= X → a* =y 2092 log decinae. logaritmo de un numero Y (positivo) en base a

Ver

Advanced Problem Solving with Logarithms

This final page focuses on applying all the previously learned concepts to solve complex logarithmic problems. It emphasizes the importance of combining multiple properties and techniques to tackle challenging exercises.

Example: Given that log_2(3) ≈ 1.585 and log_2(5) ≈ 2.322, calculate log_2(45) without using a calculator. Solution: log_2(45) = log_2(315) = log_2(3) + log_2(15) = 1.585 + log_2(35) = 1.585 + log_2(3) + log_2(5) ≈ 5.492

The page includes advanced exercises on:

  • Solving equations with multiple logarithms
  • Applying logarithmic properties to simplify complex expressions
  • Using the change of base formula in problem-solving

Highlight: Mastery of logarithmic properties and problem-solving techniques is essential for tackling advanced mathematics and real-world applications.

The page concludes with a reminder of the practical applications of logarithms in various fields, including:

  • Computer science (algorithmic complexity)
  • Finance (compound interest calculations)
  • Physics (decibel scale, earthquake magnitude)
  • Biology (population growth models)

Vocabulary: Para que sirven los logaritmos (What logarithms are used for) extends far beyond mathematical exercises, playing crucial roles in many scientific and practical applications.

Logaritmos = Introducción los coqacimos nos ayudan • Log a Ei= Y= X → a* =y 2092 log decinae. logaritmo de un numero Y (positivo) en base a

Ver

Introduction to Logarithms

This page introduces the concept of logarithms and their basic properties. Logarithms are presented as the inverse operation of exponentiation, helping to solve equations where the exponent is unknown.

Definition: A logarithm is the exponent to which a base must be raised to produce a given number.

The general form of a logarithm is expressed as:

log_a(y) = x, which is equivalent to a^x = y

Example: log_2(16) = 4 because 2^4 = 16

The page also covers the components of a logarithmic expression:

  • Base (a)
  • Argument (y)
  • Result (x)

Highlight: The most commonly used logarithmic bases are 10 (common logarithm) and e (natural logarithm, denoted as ln).

Key properties of logarithms are introduced:

  1. log_a(1) = 0
  2. log_a(a) = 1
  3. log_a(x^n) = n * log_a(x)
  4. log_a(x*y) = log_a(x) + log_a(y)
  5. log_a(x/y) = log_a(x) - log_a(y)

Vocabulary: The base of a logarithm must be positive and not equal to 1.

¿No encuentras lo que buscas? Explora otros temas.

Knowunity es la app educativa nº 1 en cinco países europeos

Knowunity fue un artículo destacado por Apple y ha ocupado sistemáticamente los primeros puestos en las listas de la tienda de aplicaciones dentro de la categoría de educación en Alemania, Italia, Polonia, Suiza y Reino Unido. Regístrate hoy en Knowunity y ayuda a millones de estudiantes de todo el mundo.

Ranked #1 Education App

Descargar en

Google Play

Descargar en

App Store

Knowunity es la app educativa nº 1 en cinco países europeos

4.9+

valoración media de la app

17 M

A los alumnos les encanta Knowunity

#1

en las listas de aplicaciones educativas de 17 países

950 K+

alumnos han subido contenidos escolares

¿Aún no estás convencido? Mira lo que dicen tus compañeros...

Usuario de iOS

Me encanta esta app [...] ¡¡¡Recomiendo Knowunity a todo el mundo!!! Pasé de un 2 a un 9 con él :D

Javi, usuario de iOS

La app es muy fácil de usar y está muy bien diseñada. Hasta ahora he encontrado todo lo que estaba buscando y he podido aprender mucho de las presentaciones.

Mari, usuario de iOS

Me encanta esta app ❤️, de hecho la uso cada vez que estudio.

Asignaturas

/

Matemáticas I

/

Ecuaciones

/

Las ecuanciones exponenciales y logarítmicas

Descubre los Logaritmos con Susi Profe: Ejercicios y Propiedades para 4 ESO y 1 Bachillerato

Logarithms are mathematical tools used to solve exponential equations. They express the power to which a base number must be raised to obtain a given value. Logaritmos Susi Profe provides a comprehensive guide on logarithmic properties and applications, covering key concepts like:

  • Definition and notation of logarithms
  • Properties of logarithms
  • Solving logarithmic equations
  • Applying logarithmic properties to simplify expressions

Key points:
• Logarithms are the inverse operation of exponentiation
• The most common bases used are 10 (common logarithm) and e (natural logarithm)
• Understanding logarithmic properties is crucial for solving complex equations
• Practical applications include modeling exponential growth and decay

...

8/3/2023

1178

 

1° Bach

 

Matemáticas I

93

Logaritmos = Introducción los coqacimos nos ayudan • Log a Ei= Y= X → a* =y 2092 log decinae. logaritmo de un numero Y (positivo) en base a

Inscríbete para ver los apuntes. ¡Es gratis!

Acceso a todos los documentos

Mejora tus notas

Únete a millones de estudiantes

Al registrarte aceptas las Condiciones del servicio y la Política de privacidad.

Applying Logarithmic Properties

This page focuses on applying the properties of logarithms to solve various problems and simplify expressions. It provides several examples and exercises to reinforce understanding.

Example: Solve log_2(8/4) = x Solution: log_2(8/4) = log_2(8) - log_2(4) = 3 - 2 = 1

The page includes exercises on:

  • Evaluating logarithms with different bases
  • Simplifying logarithmic expressions using properties
  • Solving equations involving logarithms

Highlight: When solving logarithmic equations, it's crucial to ensure that the bases are the same before applying properties.

An important concept introduced is finding the base of a logarithm when given the logarithmic equation:

Example: Find the base b in the equation log_b(125) = 3 Solution: b^3 = 125, so b = 5

The page emphasizes the importance of practice in mastering logarithmic problem-solving techniques.

Logaritmos = Introducción los coqacimos nos ayudan • Log a Ei= Y= X → a* =y 2092 log decinae. logaritmo de un numero Y (positivo) en base a

Inscríbete para ver los apuntes. ¡Es gratis!

Acceso a todos los documentos

Mejora tus notas

Únete a millones de estudiantes

Al registrarte aceptas las Condiciones del servicio y la Política de privacidad.

Advanced Logarithmic Operations

This page delves into more complex logarithmic operations and problem-solving techniques. It covers the reduction and expansion of logarithmic expressions using various properties.

Example: Reduce log(x^3 * y^2) + 2log(√z) Solution: 3log(x) + 2log(y) + log(z^(1/2))

The page provides exercises on:

  • Combining logarithms with the same base
  • Expanding logarithms of products and quotients
  • Simplifying complex logarithmic expressions

Highlight: When reducing or expanding logarithmic expressions, always ensure that the properties are applied correctly and consistently.

An important technique introduced is the use of change of base formula:

log_a(x) = log_b(x) / log_b(a)

This formula allows for the conversion between logarithms of different bases, which is particularly useful when dealing with calculators that only compute natural or common logarithms.

Vocabulary: The change of base formula is a fundamental tool in logarithmic problem-solving, especially for logaritmos neperianos (natural logarithms).

Logaritmos = Introducción los coqacimos nos ayudan • Log a Ei= Y= X → a* =y 2092 log decinae. logaritmo de un numero Y (positivo) en base a

Inscríbete para ver los apuntes. ¡Es gratis!

Acceso a todos los documentos

Mejora tus notas

Únete a millones de estudiantes

Al registrarte aceptas las Condiciones del servicio y la Política de privacidad.

Advanced Problem Solving with Logarithms

This final page focuses on applying all the previously learned concepts to solve complex logarithmic problems. It emphasizes the importance of combining multiple properties and techniques to tackle challenging exercises.

Example: Given that log_2(3) ≈ 1.585 and log_2(5) ≈ 2.322, calculate log_2(45) without using a calculator. Solution: log_2(45) = log_2(315) = log_2(3) + log_2(15) = 1.585 + log_2(35) = 1.585 + log_2(3) + log_2(5) ≈ 5.492

The page includes advanced exercises on:

  • Solving equations with multiple logarithms
  • Applying logarithmic properties to simplify complex expressions
  • Using the change of base formula in problem-solving

Highlight: Mastery of logarithmic properties and problem-solving techniques is essential for tackling advanced mathematics and real-world applications.

The page concludes with a reminder of the practical applications of logarithms in various fields, including:

  • Computer science (algorithmic complexity)
  • Finance (compound interest calculations)
  • Physics (decibel scale, earthquake magnitude)
  • Biology (population growth models)

Vocabulary: Para que sirven los logaritmos (What logarithms are used for) extends far beyond mathematical exercises, playing crucial roles in many scientific and practical applications.

Logaritmos = Introducción los coqacimos nos ayudan • Log a Ei= Y= X → a* =y 2092 log decinae. logaritmo de un numero Y (positivo) en base a

Inscríbete para ver los apuntes. ¡Es gratis!

Acceso a todos los documentos

Mejora tus notas

Únete a millones de estudiantes

Al registrarte aceptas las Condiciones del servicio y la Política de privacidad.

Introduction to Logarithms

This page introduces the concept of logarithms and their basic properties. Logarithms are presented as the inverse operation of exponentiation, helping to solve equations where the exponent is unknown.

Definition: A logarithm is the exponent to which a base must be raised to produce a given number.

The general form of a logarithm is expressed as:

log_a(y) = x, which is equivalent to a^x = y

Example: log_2(16) = 4 because 2^4 = 16

The page also covers the components of a logarithmic expression:

  • Base (a)
  • Argument (y)
  • Result (x)

Highlight: The most commonly used logarithmic bases are 10 (common logarithm) and e (natural logarithm, denoted as ln).

Key properties of logarithms are introduced:

  1. log_a(1) = 0
  2. log_a(a) = 1
  3. log_a(x^n) = n * log_a(x)
  4. log_a(x*y) = log_a(x) + log_a(y)
  5. log_a(x/y) = log_a(x) - log_a(y)

Vocabulary: The base of a logarithm must be positive and not equal to 1.

¿No encuentras lo que buscas? Explora otros temas.

Knowunity es la app educativa nº 1 en cinco países europeos

Knowunity fue un artículo destacado por Apple y ha ocupado sistemáticamente los primeros puestos en las listas de la tienda de aplicaciones dentro de la categoría de educación en Alemania, Italia, Polonia, Suiza y Reino Unido. Regístrate hoy en Knowunity y ayuda a millones de estudiantes de todo el mundo.

Ranked #1 Education App

Descargar en

Google Play

Descargar en

App Store

Knowunity es la app educativa nº 1 en cinco países europeos

4.9+

valoración media de la app

17 M

A los alumnos les encanta Knowunity

#1

en las listas de aplicaciones educativas de 17 países

950 K+

alumnos han subido contenidos escolares

¿Aún no estás convencido? Mira lo que dicen tus compañeros...

Usuario de iOS

Me encanta esta app [...] ¡¡¡Recomiendo Knowunity a todo el mundo!!! Pasé de un 2 a un 9 con él :D

Javi, usuario de iOS

La app es muy fácil de usar y está muy bien diseñada. Hasta ahora he encontrado todo lo que estaba buscando y he podido aprender mucho de las presentaciones.

Mari, usuario de iOS

Me encanta esta app ❤️, de hecho la uso cada vez que estudio.