Question 21228
log(5+x) - log(x-5)= log3
{{{log ((5+x)/(x-5)) = log 3}}}


If  {{{log M = log N}}}, then {{{M= N}}}


Therefore: {{{(5+x)/(x-5) = 3 }}}


Multiply both sides by the LCD which is (x-5):
{{{ 5+x = 3(x-5) }}}
{{{5+x = 3x -15}}}
{{{-2x = -20}}}
{{{x=10}}}


Check answers to make sure you do not have a log of any negatives.  You do not, so the answer is valid.


R^2 at SCC