\(12^2 = 144\)
So I learned that the basic log function is the inverse of exponential y = c\({^x}\)
Therefore...
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?
+2862 \(b^x=y\) 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.
