Question 446144
Use the rule {{{ log (a) - log (b) = log (a/b) }}}
{{{ log ((3 + x)) - log ((x  - 5)) = log  5 }}}
{{{ log( (3+x) / (x-5) ) = log(5) }}}
Use the rule If {{{ log(a) = log(b) }}}, then {{{ a = b }}}
{{{ (3+x) / (x-5) = 5 }}}
Multiply both sides by {{{x-5}}}
{{{ x + 3 = 5*( x - 5 ) }}}
{{{ x + 3 = 5x - 25 }}}
{{{ 4x = 28 }}}
{{{ x = 7 }}}
check answer:
{{{ log ((3 + x)) - log ((x  - 5)) = log  5 }}}
{{{ log ((3 + 7)) - log ((7  - 5)) = log  5 }}}
{{{ log(10) - log(2) = log(5) }}}
{{{ 1 - .30103 = .69897 }}}
{{{ .69897 = .69897 }}}
OK