I attempted the question in the title:
Rewrite 5^{12x-17}=125 as a logarithm. Then apply the change of base formula to solve for x using the common log. Round to the nearest thousandth.
I arrived at x=\frac{14}{12} whereas my textbook says the solution is actually this:
My working:
5^{12x-17}=125
\log_5(125)=12x-17
\frac{\ln(125)}{\ln(5)}=12x-17
3=12x-17
12x=14
x=\frac{14}{12}
Where did I go wrong and how can I arrive at \frac{5}{3}?
