algebra question

Question

\log _bx\:-\left(\log _by\:+\log _bz\right)

please show the steps

Answer 1

Hey Yittel! I am unsure as to what the question is asking, but I am assuming you are trying to simplify the expression using log rules. If that is the case, remember that adding two log expressions can be simplified by applying the product property of logs and subtracting two log expressions can be simplified by applying the quotient property of logs.

log_b x: - (log_b y: + log_b z) = log_b x: - (log_b (yz)) = log_b (x)/(yz)

Latex Expression: \log _bx\:-\left(\log _by\:+\log _bz\right) = \log _bx\:-\left(\log _b{yz}\right) = \log_b \frac{x}{yz}\right