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exponential equation-Algebra

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Solve the exponential equation. Express the solution set in terms of natural logarithms.

4^(x + 4) = 5^(2x + 5)-This question I don't understand.

  • exponential equation-Algebra -

    Alright. I think I might have gotten the answer. Write back and tell me if you think it's right. If you think I messed up, I'll keep trying.

    First use ln to rearrange the original:

    Put the exponents in front because of the properties of logs.
    Rearrange to get all the x's on one side.
    I'm sure you got to this point. But after here, it starts to get a little tricky.
    Technically, (ln5)/(ln4) is equal to [(ln5)/(ln4)]/1 right?
    Let's set a about "u" equal to the numerator of this fraction.
    So... u=[(ln5)/(ln4)]
    Let's plug that back in to what we had from before:
    Use cross multlipication to get this:
    Distribute the u
    Get all the parts with x's on one side:
    Pull out an x:
    Divide the (5u-4) by (1-2u) to get x by itself:
    Plug the u value back in and simplify
    x=(5((ln5)/(ln4))-4) / (1-2((ln5)/(ln4))
    I think that's as far as you can go.

    Good luck! :-)

  • exponential equation-Algebra -

    the closest answers that I have that are given in the multiple choice is {5 ln 5 - 4 ln 4/ln 4-2 ln 5}

  • exponential equation-Algebra -

    Take the natural logs (ln) of both sides.
    (x+4) ln 4 = (2x+5) ln 5
    x ln 4 + 4 ln 4 = 2x ln 5 + 5 ln 5
    x (2 ln 5 - ln 4) = 4 ln 4 - 5 ln 5
    x = (4ln4 - 5ln5)/(2ln5 - ln4)
    This becomes the same as your answer if you multiply both numerator and denominiator by -1

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