How do you solve #log_ 2 (x+2) - log_2 (x-5) = 3#?

1 Answer
Helen D.
Mar 18, 2016

same base so you can add the log terms
log2 #(x+2)/(x-5# =3
so now you can convert this to exponent form:
We will have
#(x+2)/(x-5)=2^3#
or

#(x+2)/(x-5)=8# which is pretty simple to solve since

x + 2 = 8(x - 5)
7x = 42
x = 6

quick check by substitution to the original equation will confirm solution.

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