# Use a calculator and the change-of-base formula to evaluate {eq}\log_{30} 339 {/eq} to 4 decimal places.

## Question:

Use a calculator and the change-of-base formula to evaluate {eq}\log_{30} 339 {/eq} to 4 decimal places.

## Change of Base Formula

Since the logarithm is the inverse of the exponential function, there are as many logarithms are there are numbers! It's not possible to create a calculator that can evaluate every possible logarithm, so most have the two common ones: the natural logarithm (base e) and the logarithm with base ten. Thankfully, we can use these to find the value of any logarithm using the change of base formula.

{eq}log_a b = \frac{\ln b}{\ln a} = \frac{\log_{10} b}{\log_{10} a} {/eq}

## Answer and Explanation: 1

Become a Study.com member to unlock this answer!

In order to use the change of base formula, we need to use either the natural log or the base ten logarithm. Both will give the same answer. We then...

See full answer below.

Change Of Base Formula: Logarithms & Proof

from

Chapter 1 / Lesson 13
4.5K

Define the logarithm and change of base. Prove the change of base formula. Learn how to rewrite logarithms using the change of base formula with examples.