Use logarithms to solve 4^2x+1=25

First, we want to combine like terms.

The way we do this is by subtracting 1 from both sides.

4^2x = 24

Second, we can take the natural log (ln) of both sides. This will allow us to drop down the 2x out of the exponent in front of the natural log as displayed below.

ln|4^2x| = ln|24| becomes 2xln|4| = ln|24|

Then we can divide both sides by 2ln|4| to isolate x on the left side. Any of the below answers are acceptable. (I got the different answers using logarithmic rules)

x = ln|24| / 2ln|4| = 2ln|24/4| = 2ln|6| = ln|6^2| = ln|36|