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Chapter 4: Problem 28

Evaluate each expression without using a calculator. $$\log _{3} \frac{1}{9}$$

Short Answer

Expert verified
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Step by step solution

01

Understanding the Logarithm

In a logarithmic expression \(\log_b a = n\), 'b' is the base, 'a' is the number and 'n' is the exponent to which the base must be raised to obtain the number. So, \(\log _{b} a = n\) is equivalent to \(b^n = a\).
02

Reshape the Number

Given the number as 1/9, it can be written as \(3^{-2}\) since \(3^{-2} = 1/(3^2) = 1/9\).
03

Evaluate the Expression

Substitute \(3^{-2}\) in place of 1/9 in the original expression, so we get \(\log_3{(3^{-2})}\). Now according to the logarithm rule, the expression equals to -2.

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