Advanced Functions math

Could someone help me with this question?

5^(2x) - 4^(5^x) = 12

I got up to log (5^x)= log(-4)
but it isnt correct since it can't be negative.

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  1. I don't know if this will show up properly, but do you mean

    52x - 45x = 12 ?

    How did you get log(5^x) = log(-4) ??

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  2. Yes

    to get that i did:

    (5^x)^2 - 4(5^x) =12

    5^x(1-4) = 12

    -3(5^x)= 12

    log(5^x) = log(-4)

    If you could show me the correct way to do it, that would be great! thanks!

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  3. ah, but now you changed the question.
    In the original you had 4 raised to the (5 raised to the x) in the middle term
    Now you have 4(5^x)

    This last version makes it easy, the first version would be a nightmare.

    If it is
    (5^x)^2 - 4(5^x) =12

    then let's let y = 5^x
    our equation now becomes
    y^2 - 4y = 12 which is a nice quadratic
    y^2 - 4y - 12 = 0
    (y-6)(y+2) = 0
    so y = 6 or y = -2

    then 5^x = 6
    log (5^x) = log6
    xlog5 = log6
    x = log6/log5 = 1.11328

    or 5^x = -2
    xlog5 = log(-2) which is undefined, thus no solution for that part

    so x = appr. 1.113

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  4. The original question was what i needed to solve, but with the way i changed it, is it correct?

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  5. My answer, if substituted into the second version of the equation, satisfies it.

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