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28 June, 17:39

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

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Answers (2)
  1. 28 June, 19:41
    0
    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))
  2. 28 June, 19:49
    0
    ln 5 / ln 5 - 2 ln 2

    Step-by-step explanation:

    I took the test
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