Chapter 12: Q39. (page 637)

Evaluate each expression.
$\log_{9} 3$

Short Answer

Expert verified

The value of $\log_{9} 3 = \frac{1}{2}$ .

Step by step solution

Step 1. Given Information.

Given, to evaluate the expression $\log_{9} 3$ .

Step 2. Calculation.

According to the properties of logarithms, $\log_{b} a^{n} = n \log_{b} a, \log_{a} a = 1$

Simplifying the expression:

$\begin{array}{l} \log_{9} 3 = \log_{9} \sqrt{9} \\ \log_{9} 3 = \log_{9} {(9)}^{\frac{1}{2}} \\ \log_{9} 3 = \frac{1}{2} \log_{9} (9) \\ \log_{9} 3 = \frac{1}{2} (1) \\ \log_{9} 3 = \frac{1}{2} \end{array}$

Step 3. Conclusion.

Hence, $\log_{9} 3 = \frac{1}{2}$ .

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Evaluate each expression.
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