Write the fraction you would use to change the base for {eq}{{\log }_{8}}15 {/eq}.

Question:

Write the fraction you would use to change the base for {eq}{{\log }_{8}}15 {/eq}.

Logarithms: Base Conversions

Among other useful properties, there is a formula which might be used to change the base of a given logarithm to any other base we desire. For a logarithm in a form of {eq}log_a (b) {/eq}, let's say that we desire to change the base from a to some base x. According to the property, the fraction would be:

{eq}log_a (b) = \frac{log_x (b)}{log_x (a)} {/eq}.

Answer and Explanation: 1

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For this problem, we're given a base of 8 of the logarithm.

Assume that we wish to change it to any other base, for example, let's label that base a....

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Learn more about this topic:

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.