Question 59700
Your algebraic solution is ok.
To graph this, you want to get your equation into a form like: f(x) = ...., so:
{{{4^(3x-1) = 90}}} subtract 90 from both sides.
{{{f(x) = 4(3x-1) - 90}}}
Now you can enter this function, as {{{y = 4^(3x-1) - 90}}} into your graphing calculator. 
{{{graph(300,200,-5,5,-5,5,4^(3x-1)-90)}}}

The solution is the intersection of the line and the x-axis or x = 1.4...