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\(12^2 = 144\)


So I learned that the basic log function is the inverse of exponential y = c\({^x}\)


y = c\({^x}\)

x = c\({^y}\)

log\({_c}\)x = log\({_c}\)c\({^y}\) (the log & c cancel...)

log\({_c}\)x = y


When I applied this to \(12^2 = 144\) I got log\({_{12}}\)2 = 144 while the answer in the textbook is log\({_{12}}\)144 = 2.


What did I do wrong?

 Apr 23, 2019

\(b^x=y\) is the exponential form.


\(log_by=x\) is the log form.


The exponential form is \(12^2=144\).


You likely switched the X and Y when you wrote the log formula.


So since the y is 144,


you were supposed to have \(log_{12}\boxed{144}=2\)


The 144 is the part you messed up, as you switched the x and y.

 Apr 23, 2019

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