\(12^2 = 144\)

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?

Guest Apr 23, 2019

#1**+2 **

\(b^x=y\) 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.

CalculatorUser Apr 23, 2019