SOLUTION: Express the inverse function of y=e^(4x-5) in the form y=a ln x +b. We are looking for the coefficients a and b. I have come up with y=1/4 ln x +5. the 5 seems to be wrong. Any

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Express the inverse function of y=e^(4x-5) in the form y=a ln x +b. We are looking for the coefficients a and b. I have come up with y=1/4 ln x +5. the 5 seems to be wrong. Any       Log On


   

Question 60450: Express the inverse function of y=e^(4x-5) in the form y=a ln x +b. We are looking for the coefficients a and b. I have come up with y=1/4 ln x +5. the 5 seems to be wrong. Any information on this would be helpful.
Answer by hayek(51) About Me  (Show Source):
You can put this solution on YOUR website!
It looks like you dropped a parentheses, here is the solution:
y=e%5E%284x-5%29
Substitute y and x to find the inverse function:
x=e%5E%284y-5%29
Take ln of both sides:
ln%28x%29=4y-5
Solve for y:
4y=ln%28x%29%2B5
y=%281%2F4%29%2A%28ln%28x%29%2B5%29
y=ln%28x%29%2F4+%2B+5%2F4
So, highlight%28a=1%2F4%29 and highlight%28b=1%261%2F4%29.
Here are the graphs of the original equation and the inverse, with y=x drawn to show the inverse symmetry.
graph%28300%2C200%2C-1%2C2%2C-1%2C2%2C2.71828%5E%284x-5%29%2Cln%28x%29%2F4+%2B+5%2F4%2C+x%29