Question

How can I express logbx-(logby+logbz) as a single log?

Answer 1

$\bf log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y) \\ \quad \\ % Logarithm of rationals log_{{ a}}\left( \frac{x}{y}\right)\implies log_{{ a}}(x)-log_{{ a}}(y)\\\\ -----------------------------\\\\ log_b(x)-[log_b(y)+log_b(z)]\implies log_b(x)-[log_b(yz)] \\\\\\ log_b\left( \cfrac{x}{yz} \right)$