Rearranging Equations – Working with Logarithms

Let’s bring logarithms into the equation (see what I did there?!).

How do we rearrange this equation to solve for r?

L o g space left parenthesis r right parenthesis space equals space fraction numerator G space minus space increment C over denominator straight pi end fraction

We should remember from earlier that the inverse operation of taking a logarithm is exponentiation. As we are using a base 10 log, we exponentiate both sides (make them powers of 10). This cancels the log of r and makes the fraction numerator G space minus space increment C over denominator straight pi end fraction the exponent of 10 as shown below:

r space equals space 10 to the power of open parentheses fraction numerator G space minus space increment C over denominator straight pi end fraction close parentheses end exponent space

Had this been a natural log, it would look like this:

l n space left parenthesis r right parenthesis space equals space fraction numerator G space minus space increment C over denominator straight pi end fraction

And becomes:

r space equals e to the power of open parentheses fraction numerator G space minus space increment C over denominator straight pi end fraction close parentheses end exponent space

To help reinforce what we have just learned, on the next page there are some practice questions. Answers and explanations can be revealed by clicking on show answer.

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