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 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 $\frac{5}{3}$?

In your 4th step, you said $3 = 12x - 17$ then in your 5th step, you said $12x = 14,$ when it's actually $12x = 17 + 3 = 20.$ So, $x = \boxed{\frac{5}{3}}$
