There is this question

Solve for x in the following exponential an logarithmic equations

The solution is as follows

First use Product Rule to get

Then use Inversion Rules to get

Thus

And from there I can get the x values

While I understand the product rule I am not sure what is happening when using the inverse rule. I am unsure of where the "log" sign goes or where the number 3 comes from. Any sort of advice as to how you get these equations would be very helpful. Thank you