Question

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

Answer 1

Answer:

ln 5 / ln 5 − 2 ln 2

Step-by-step explanation:

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Answer 2

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))