Answer:
log₇(xy/z)
Step-by-step explanation:
We know that
[tex]\log_ax = b \implies a^b = x[/tex]
we also know that:
[tex]a^b \cdot a^c = a^{b + c}[/tex]
so it follows that
[tex]\log_ax + log_ay = log_a(xy)[/tex]
from:
[tex]\frac{a^b}{a^c} = a^{b - c}[/tex]
follows that
[tex]\log_ax - log_ay = log_a(\frac{x}{y})[/tex]
so
[tex]\log_7x + \log_7y - \log_7z = \log_7(xy) - \log_7z = \log_7(\frac{xy}{z})[/tex]
