Question

How to change the expression to a single logarithm

Answer 1

First, you'll use the "Log power rule," which says that $\log_ax^p=p\log_ax$. In this case, you're going from the form on the right (with p in front of the log) to the form on the left (with p in the exponent position). So, the expression becomes:

$\log_7x^4+\log_7y^8+\log_7z^4$

Then, you'll use the "Log product rule," which says that $\log_a(xy)=\log_ax+\log_ay$. Again, you're going from the form on the right to the form on the left (basically, from the sum of the logs, to a log of the products). So you get:

$\log_7(x^4y^8z^4)$

There's your expression simplified into a simple logarithm.