# How to write an exponential equation into logarithmic form

Blake C. Notice these are equivalent statements. See the image below to see what this technique looks like. The round-about technique also works to go the other way, from logarithmic form to exponential form.

## Logarithmic equations

The round-about technique also works to go the other way, from logarithmic form to exponential form. In the logarithmic form we are most often solving for the missing exponent, having been given the base a and the resultant y. This is one way to think about it is saying the power that I need to raise 5 to to get to 1 over is equal to negative 3 or that 5 to the negative 3 power is equal to 1 over In this expression, some number a raised to the x power equals y. This is saying that the power I need to raise 10 to to get to is equal to 2. Which is the same thing as saying that 10 to the 2nd power is Thankfully, there is an easy trick for this translation process. And we can verify that this has formatted it the right way.

This is is logarithmic form. Logarithmic form and exponential form. And the way that I specify the base is by doing this underscore right over here. This is one way to think about it is saying the power that I need to raise 5 to to get to 1 over is equal to negative 3 or that 5 to the negative 3 power is equal to 1 over Problems involving this form may ask for any missing value, but usually this form is used when we have been given the value of a and x, and are asked to compute y. Which is the same thing as saying that 10 to the 2nd power is So this is log base 5 of 1 over is equal to negative 3.

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