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Chapter 3: Problem 22

Evaluate the logarithm using the change-of-base formula. Round your result to three decimal places. $$\log _{3} 0.015$$

Short Answer

Expert verified
The solution is approximately \(-2.385\) after rounding to three decimal places.

Step by step solution

01

Identify the Given Values

The given values are the base, which is 3, and the logarithm, which is 0.015.
02

Apply the Change of Base Formula

Apply the change-of-base formula, which is \(\log_b a = \frac{\log a}{\log b}\). Here, a is 0.015 and b is 3, so the formula becomes \(\log_3 0.015 = \frac{\log 0.015}{\log 3}\).
03

Evaluate the Expression

Use a calculator or logarithm table to find the values of \(\log 0.015\) and \(\log 3\). Divide the result of \(\log 0.015\) by the result of \(\log 3\).
04

Round the Answer

As per the question, round the answer to three decimal places.

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