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

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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...

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Change Of Base Formula: Logarithms & Proof

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Chapter 1 / Lesson 13
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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.