Question 1132903
Find the inverse function for

{{{ f(x) = (ln(x)-5)/(2ln(x)+7) }}}


{{{ y= (ln(x)-5)/(2ln(x)+7) }}}...........swap {{{x}}} and {{{y}}}


{{{ x= (ln(y)-5)/(2ln(y)+7) }}}.......solve for {{{y}}}


{{{ x(2ln(y)+7)= (ln(y)-5) }}}


{{{ 2xln(y)+7x= ln(y)-5 }}}


{{{ 2xln(y)- ln(y)=-5 -7x}}}


{{{ (2x- 1)ln(y)=-5 -7x}}}


{{{ ln(y)=(-5 -7x)/(2x- 1)}}}


Apply  log rule: {{{a=log(b,b^a)}}}


{{{ ln(y)=ln(e^((-5 -7x)/(2x- 1)))}}}->When the logs have the same base

{{{highlight(y = e^((-5 -7x)/(2x- 1)))}}}



{{{ graph( 600, 600, -15, 15, -15, 15, (ln(x)-5)/(2ln(x)+7),e^((-5 -7x)/(2x- 1))) }}}