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Math Help - X in exponent on both sides, can't make bases the same

  1. #1
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    X in exponent on both sides, can't make bases the same

    Help:

    7^-^4^x = 2^1^+^3^x
    I should take the ln of both sides, right...?
    -4x ln 7 = (1+3x) ln 2

    How do I simplify?
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  2. #2
    A Plied Mathematician
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    I would distribute out the RHS first. Your goal, as always is to get the terms with x's on one side, and all the other terms on the other.
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  3. #3
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    You don't want to simplify, you want to solve the equation. Step back and look at what you have written, remember that ln7 and ln2 are just numbers.
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  4. #4
    Senior Member eumyang's Avatar
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    Quote Originally Posted by jimmy1 View Post
    Help:

    7^-^4^x = 2^1^+^3^x
    I should take the ln of both sides, right...?
    -4x ln 7 = (1+3x) ln 2

    How do I simplify?
    \begin{aligned}<br />
7^{-4x} &= 2^{1 + 3x} \\<br />
-4x \ln 7 &= (1+3x) \ln 2 \\<br />
-4x \ln 7 &= \ln 2 + 3x \ln 2 \\<br />
3x \ln 2 + 4x \ln 7 &= -\ln 2 \\<br />
x(3\ln 2 + 4\ln 7) &= -\ln 2 ... \\<br />
\end{aligned}

    Can you finish?
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