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)#?

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Answer 1 · 2015-07-05T23:24:07

#log_5(25/x) = 2 - log_5x#

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(x^d) =dlog_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#