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Chapter 33: Problem 959

Find the logarithm of \(3^{2}\)

Short Answer

Expert verified
\(log(3^2) = 2 * log(3) \approx 0.9542\)

Step by step solution

01

Understanding the logarithm

To find the logarithm of a number, we need to know the base of the logarithm. Since the exercise doesn't specify the base, let's assume the most common base, base 10, known as the common logarithm. The logarithm is the inverse of the exponential function, which means that: \[log_b(x^y) = y * log_b(x)\] Where `b` is the base, `x` is the number we are taking the logarithm of, and `y` is the exponent.
02

Apply the logarithm properties

Now, we need to find the logarithm of \(3^2\) using base 10. According to the logarithm properties explained in Step 1, we can rewrite the expression as: \(log(3^2) = 2 * log(3)\)
03

Find the value of each logarithm

To find the value of each logarithm, we can use a calculator or look up logarithm tables. In this case, we need to find the value of \(log(3)\). Using a calculator, we find: \(log(3) \approx 0.4771\)
04

Final calculation

Now that we have the value of \(log(3)\), let's substitute it back into our expression: \(2 * log(3) = 2 * 0.4771 = 0.9542\) Thus, the logarithm of \(3^2\) to base 10 is approximately 0.9542.

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