What is x if #log_2 (x+5) - log_2(x-2) +2= 3#?

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Answer 1 · 2015-10-23T10:57:50

#x=9#

Given
#log_2(x+5)-log_2(x-2)+2=3#

Subtract #2# from both sides
#log_2(x+5)-log_2(x-2)=1#

Difference of log's is log of quotient (a basic logarithmic rule)
#log_2((x+5)/(x-2))=1#

By definition of logarithm
#2^1 = (x+5)/(x-2)#

Algebraic simplification from here on
#2(x-2) = x+5#

#2x-4 = x+5#

#x=9#