Question 60450
It looks like you dropped a parentheses, here is the solution:

{{{y=e^(4x-5)}}}
Substitute y and x to find the inverse function:
{{{x=e^(4y-5)}}}
Take ln of both sides:
{{{ln(x)=4y-5}}}
Solve for y:
{{{4y=ln(x)+5}}}
{{{y=(1/4)*(ln(x)+5)}}}
{{{y=ln(x)/4 + 5/4}}}
So, {{{highlight(a=1/4)}}} and {{{highlight(b=1&1/4)}}}.

Here are the graphs of the original equation and the inverse, with y=x drawn to show the inverse symmetry.
{{{graph(300,200,-1,2,-1,2,2.71828^(4x-5),ln(x)/4 + 5/4, x)}}}