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Math Help - Can it be simplified more?

  1. #1
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    Can it be simplified more?

    Hi

    Solving leaving the answer in term of e or ln

    (5^3+x) = (20^x-3)

    ln 5 (3 + x) = ln 20 (x - 3)

    3 ln5 + x ln5 = x ln20 - 3 ln20

    3 ln5 + 3 ln20 = x(ln20 - ln5)

    can it be simplified more?
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    ln(20)=ln(4*5)=ln(4)+ln(5)=ln(2^2)+ln(5)=2ln2+ln(5 )
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  3. #3
    Senior Member eumyang's Avatar
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    Quote Originally Posted by danielh9103 View Post
    Hi

    Solving leaving the answer in term of e or ln

    (5^3+x) = (20^x-3)

    ln 5 (3 + x) = ln 20 (x - 3)

    3 ln5 + x ln5 = x ln20 - 3 ln20

    3 ln5 + 3 ln20 = x(ln20 - ln5)

    can it be simplified more?
    You should start learning LaTeX - this is hard to read. I assume that you mean
    5^{3 + x} = 20^{x - 3}

    So,
    \begin{aligned}<br />
\ln 5^{3 + x} &= \ln 20^{x - 3} \\<br />
3 \ln 5 + x \ln 5 &= x \ln 20 - 3 \ln 20 \\<br />
3 \ln 5 + 3 \ln 20 &= x(\ln 20 - \ln 5)<br />
\end{aligned}

    This is what you wrote so far. But you're not done yet...
    \begin{aligned}<br />
3 (\ln 5 + \ln 20) &= x(\ln 20 - \ln 5) \\<br />
3 \ln 100 &= x \ln 4 \\<br />
x &= \frac{3 \ln 100}{\ln 4} \\<br />
x &= \frac{6 \ln 10}{\ln 4} \\<br />
\end{aligned}
    Last edited by eumyang; July 29th 2010 at 06:34 AM. Reason: OP stated that answer needs to be in terms of e or ln
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