What is the exact solution to the equation 2^2x=5^x-1?

ln 5 / ln 5 - 2 ln 2

Step-by-step explanation:

I took the test

2^2x=5^x-1

Take the log pf both sides:

ln (2^2x) = ln (5^x-1)

Expand the logs by pulling the exponents out:

2xln (2) = (x-1) ln (5)

Simpligy the right side:

2xln (2) = ln (5) x - ln (5)

Now solve for x:

Subtract ln (5) x from both sides:

2xln (2) - ln (5) x = - ln (5)

Factor x out of 2xln (2) - ln (5) x

x (2ln (2) - ln (5)) = - ln (5)

Divide both sides by (2ln (2) - ln (5))

X = - ln (5) / (2ln (2) - ln (5))