Statement
The difference of two logarithms with the same base is just one logarithm with the inside parts being divided.
$$ \log_a(b) - \log_a(c) = \log\left(\frac{b}{c}\right) $$
Proof
Write the difference as a sum.
$$ \log_a(b) + -1 * \log_a(c) $$
Use the logarithm power rule to write the following.
$$ \log_a(b) + \log_a(c^{-1}) $$
Now use the logarithm sum rule to combine the logarithms.
$$ \log_a(b * c^{-1}) $$
Finally, write the negative exponent as a fraction.
$$ \log_a\left(\frac{b}{c}\right) $$