How do you condense #1/2log_8(x+5)-3log_8(y)#?

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Answer 1 · 2016-04-12T00:43:12

In this problem, the following log rules will be used:

#alogn = logn^a#

#log_na - log_nb = log_n(a/b)#

Since #x^(1/2)# = #sqrt(x)# (by the rule #a^(n/m) = root(n)(a^m)#):

#log_8sqrt(x + 5) - log_8(y^3)#

#log_8((sqrt(x + 5))/(y^3))#

Thus, you have your answer, in simplest form.

Hopefully this helps.