# How do you write the logarithmic expression as the sum, difference, or multiple of logarithms and simplify as much as possible for log_5(25/x)?

Jul 5, 2015

${\log}_{5} \left(\frac{25}{x}\right) = 2 - {\log}_{5} x$

#### Explanation:

Property: log_b(x/y) = log_b x – log_b y

So

log_5(25/x) = log_5(25) – log_5x

log_5(25/x) = log_5(5^2) – log_5x

Property: ${\log}_{b} \left({x}^{d}\right) = \mathrm{dl} o {g}_{b} x$

So

log_5(25/x) = log_5(5^2) – log_5x = 2log_5(5) – log_5x

log_5(25/x) = = (2×1) – log_5x

log_5(25/x) = = 2 – log_5x