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

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Answer 1 · 2016-03-18T14:04:29

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.

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