Question

Use the property: $b^{a}=c$ if and only if $\log _{b}(c)=a$ from Theorem 6.2 to rewrite the given equation in the other form. That is, rewrite the exponential equations as logarithmic equations and rewrite the logarithmic equations as exponential equations. $\log _{3}\left(\frac{1}{81}\right)=-4$

Name: Problem 10, Chapter 6: Precalculus
Uploaded: 2021-08-14T14:09:12-08:00
Duration: 31 s
Channel: Nick Johnson
Description: Use the property: b^a=c if and only if logb(c)=a from Theorem 6.2 to rewrite the given equation in the other form. That is, rewrite the exponential equations as logarithmic equations and rewrite the logarithmic equations as exponential equations. log3((1)/(81))=-4

   Use the property: $b^{a}=c$ if and only if $\log _{b}(c)=a$ from Theorem 6.2 to rewrite the given equation in the other form. That is, rewrite the exponential equations as logarithmic equations and rewrite the logarithmic equations as exponential equations.
$\log _{3}\left(\frac{1}{81}\right)=-4$

Precalculus

Carl Stitz, Jeff… 3rd Edition

Chapter 6, Problem 10

Instant Answer

Solved by Expert Nick Johnson

08/14/2021

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Step 1: We start with the given logarithmic equation $\log _{3}\left(\frac{1}{81}\right)=-4$. Show more…

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Use the property: $b^{a}=c$ if and only if $\log _{b}(c)=a$ from Theorem 6.2 to rewrite the given equation in the other form. That is, rewrite the exponential equations as logarithmic equations and rewrite the logarithmic equations as exponential equations. $\log _{3}\left(\frac{1}{81}\right)=-4$

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Key Concepts

Definition of Logarithms

A logarithm is defined as the exponent to which a base must be raised to yield a given number. This means that if log?b?(c) = a, then b raised to the power of a equals c, which establishes the inverse relationship between exponentiation and logarithms.

Conversion between Exponential and Logarithmic Forms

This is the property that allows us to switch between the logarithmic and exponential forms of an equation. Specifically, the equation b^a = c can be rewritten as log?b?(c) = a, and vice versa. This conversion is fundamental in solving equations and understanding the structure of logarithmic and exponential functions.

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