Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Converting Exponential Equations to Logarithmic Form**
**Example Problem:**
Given the exponential equation:
\[ x^y = z \]
Convert this exponential equation into its logarithmic form.
**Solution:**
To convert an exponential equation \( x^y = z \) into a logarithmic equation, use the following definition of a logarithm:
\[ \log_b(a) = c \text{ is equivalent to } b^c = a \]
Using this definition, the equivalent logarithmic form of the given exponential equation \( x^y = z \) is:
\[ \log_x(z) = y \]
In summary,
\[ x^y = z \text{ converts to } \log_x(z) = y \]
**Practice Question:**
Convert the following exponential equation into a logarithmic equation:
\[ 2^4 = 16 \]
**Incorrect Attempt:**
Answer provided: \[ 1 \]
This answer is incorrect. Applying the correct conversion rule,
The correct logarithmic form is:
\[ \log_2(16) = 4 \]
Understanding how to convert between exponential and logarithmic forms is fundamental in various math and science disciplines. Keep practicing to master these conversions!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c8e8955-7b00-44a9-a272-a38b187e6aa8%2F821950da-8262-40fa-9b6e-23dada103e42%2F90twifk_processed.png&w=3840&q=75)
Transcribed Image Text:**Converting Exponential Equations to Logarithmic Form**
**Example Problem:**
Given the exponential equation:
\[ x^y = z \]
Convert this exponential equation into its logarithmic form.
**Solution:**
To convert an exponential equation \( x^y = z \) into a logarithmic equation, use the following definition of a logarithm:
\[ \log_b(a) = c \text{ is equivalent to } b^c = a \]
Using this definition, the equivalent logarithmic form of the given exponential equation \( x^y = z \) is:
\[ \log_x(z) = y \]
In summary,
\[ x^y = z \text{ converts to } \log_x(z) = y \]
**Practice Question:**
Convert the following exponential equation into a logarithmic equation:
\[ 2^4 = 16 \]
**Incorrect Attempt:**
Answer provided: \[ 1 \]
This answer is incorrect. Applying the correct conversion rule,
The correct logarithmic form is:
\[ \log_2(16) = 4 \]
Understanding how to convert between exponential and logarithmic forms is fundamental in various math and science disciplines. Keep practicing to master these conversions!
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