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Math Help - Solving functions equation

  1. #1
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    Solving functions equation

    Need help with the following.

    Solving functions equation-screen-shot-2013-05-12-8.38.05-pm.png

    Thanks
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Solving functions equation

    a) 25^{x-3}=5^x

    You can get the same base here since 25=5^2, so that you may write:

    (5^2)^{x-3}=5^x

    5^{2(x-3)}=5^x

    Now equate exponents, and solve for x.

    b) 2\left(\frac{1}{2} \right)^x-\left(\frac{1}{4} \right)^x=1

    Use the substitution u=\left(\frac{1}{2} \right)^x so that you may nor write:

    2u-u^2=1

    Now, solve the resulting quadratic, then back substitute for u.

    c) 3\ln(2x+5)=9

    Divide through by 3 to get:

    \ln(2x+5)=3

    Now convert from logarithmic to exponential form and solve for x.

    d) e^{(x-2)^2}=2

    Convert from exponential to logarithmic form:

    (x-2)^2=\ln(2)

    Now solve for x using the square root property.

    e) 6^{-7x}=5

    Take the natural log of both sides to get:

    -7x\ln(6)=\ln(5)

    Now solve for x.
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