Problem 61 - Introductory and Intermediate Algebra for College Students 4th

Question

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. $$\log _{5} 13$$

Step-by-Step Solution

Answer

Find the value of \[\frac{\log 13}{\log 5}\] using your calculator and make sure to round your answer to four decimal places.

Step 1: Applying the Logarithm Base Change Formula

The first step is to apply the logarithm base change formula to convert the base of the logarithm. Apply the formula \[\log _{b} a = \frac{\log a}{\log b}\] where a = 13 and b = 5. It would look like this: \[\log _{5} 13 = \frac{\log 13}{\log 5}\]

Step 2: Evaluating the Right Side

Next, evaluate the right-hand side using a calculator. It doesn't matter whether you use the natural logarithm or the common logarithm, but do ensure to use the same logarithm for both the numerator and denominator.

Step 3: Rounding the Result to Four Decimal Places

After obtaining the resultant value, round it up to four decimal places as the problem requested.