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
$2(x-2) = x+5$

$2x-4 = x+5$

$x=9$

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