How do you solve ${log}_{3} x - {log}_{3} (x + 5) = 3$ $log_3 x-log_3(x+5)=3$ ?

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Answer 1 · 2016-09-11T12:28:32

$x = - \frac{135}{26} = 5 \frac{5}{26}$ $x = -135/26 = 5 5/26$

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

${log}_{3} (\frac{x}{x + 5}) = 3$ $log_3 (x/(x+5) )= 3$

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

${log}_{3} 3 = 1 \to 3 {log}_{3} 3 = 3 \times 1 = 3$ $log_3 3 =1 " " rarr 3log_3 3 =3xx1 = 3$

${log}_{3} (\frac{x}{x + 5}) = 3 {log}_{3} 3$ $log_3 (x/(x+5) )= 3log_3 3$

${log}_{3} (\frac{x}{x + 5}) = {log}_{3} 3^{3}$ $log_3 (x/(x+5) )= log_3 3^3$

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

$27(x+5) = x$

$27x +135 = x$

$26x = -135$

$x = -135/26$

How do you solve log_3 x-log_3(x+5)=3log3x−log3(x+5)=3log_3 x-log_3(x+5)=3?