First, you'll use the "Log power rule," which says that [tex]\log_ax^p=p\log_ax[/tex]. 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:
[tex]\log_7x^4+\log_7y^8+\log_7z^4[/tex]
Then, you'll use the "Log product rule," which says that [tex]\log_a(xy)=\log_ax+\log_ay[/tex]. 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:
[tex]\log_7(x^4y^8z^4)[/tex]
There's your expression simplified into a simple logarithm.
