Question 1052013
{{{ log(( 5x - 1 )) = 2 + log(( x - 2 )) }}}
Express {{{ 2 }}} as a log
{{{ log(( 5x - 1 )) = log(( 100 )) + log(( x-2 )) }}}
{{{ log(( 5x - 1 )) = log(( 100*( x - 2 ) )) }}}
{{{ 5x - 1 = 100*( x-2 ) }}}
{{{ 5x - 1 = 100x - 200 }}}
{{{ 95x = 199 }}}
{{{ x = 199/95 }}}
{{{ x = 2.0947 }}}
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Check answer:
{{{ log( 5*(199/95) - 1 ) = 2 + log( 199/95 - 2 ) }}}
{{{ log( 199/19 - 19/19 ) = 2 + log( 199/95 - 190/95 ) }}}
{{{ log( 180/19 ) = 2 + log( 9/95 ) }}}
{{{ log( 180 ) - log( 19 ) = 2 + log( 9 ) - log( 95 ) }}}
{{{ 2.2553 - 1.2788 = 2 + .9542 - 1.9777 }}}
{{{ .9765 = .9765 }}}
OK