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# Relationship between exponentials & logarithms

Video transcript

Voiceover:Rewrite the following equation in logarithmic form. So they wrote 100 is equal to 10 to the second power. So if we wanna write the same information, really, in logarithmic form, we could say that the power that I need to raise 10 to to get
to 100 is equal to 2, or log base 10 of 100 is equal to 2. Notice these are equivalent statements. This is just in exponential form. This is is logarithmic form. This is saying that the power I need to raise 10 to to get
to 100 is equal to 2. Which is the same thing as saying that 10 to the 2nd power is 100. 10 to the second power is 100. And the way that I specify the base is by doing this
underscore right over here. So underscore 10, log base 10 of 100 is equal to 2. Here they ask us to rewrite the following equation in exponential form. So this is log base 5 of 1 over 125 is equal to negative 3. This is one way to
think about it is saying the power that I need to raise 5 to to get to 1 over 125
is equal to negative 3 or that 5 to the negative 3 power is equal to 1 over 125. And we can verify that this has formatted it the right way. 5 to the negative 3 power is 1 over 125. The exact same truth about the universe, just in different forms. Logarithmic form and exponential form. So let me check my answer and make sure I got it right. And I did.