Question

Convert the following expressions to the indicated base. \(\ln |x|\) using base 5

Short answer

Question: Convert the given expression \(\ln |x|\) to base 5. Answer: \(\log_5 |x| = \frac{\ln |x|}{\ln 5}\)

Step-by-step solution

Identify the given expression

The given expression is: \(\ln |x|\)

Use the change of base formula

We apply the change of base formula to the given expression. In this case, 'a' is 5, 'b' is |x|, and 'c' is 'e' (since \(\ln\) is a natural logarithm, which is base 'e'): \(\log_5 |x| = \frac{\ln |x|}{\ln 5}\)

Write the final expression

The given expression \(\ln |x|\) converted to base 5 is: \(\log_5 |x| = \frac{\ln |x|}{\ln 5}\)