How do you solve $log_3 x-log_3(x+5)=3$ ?

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Answer 1 · 2016-09-11T12:28:32

$x = -135/26 = 5 5/26$

"If the log terms are being subtracted, then the numbers are being divided"

$log_3 (x/(x+5) )= 3$

"Both sides must be logs, or both sides must be numbers"

$log_3 3 =1 " " rarr 3log_3 3 =3xx1 = 3$

$log_3 (x/(x+5) )= 3log_3 3$

$log_3 (x/(x+5) )= log_3 3^3$

$:. x/(x+5) =27/1 " "(3^3 = 27)$

$27(x+5) = x$

$27x +135 = x$

$26x = -135$

$x = -135/26$

How do you solve log_3 x-log_3(x+5)=3log_3 x-log_3(x+5)=3?