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Math Help - How to solve for an exponent...

  1. #1
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    How to solve for an exponent...

    Can you show me how to solve for n in the equation:

    60000= 38400(1.07)^n


    Thank you.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by oryxncrake View Post
    Can you show me how to solve for n in the equation:

    60000= 38400(1.07)^n


    Thank you.
    First simplify a bit

    25=16(1.07)^n

    Now take nat. logs of both sides

    \ln{25}=\ln{\left[16(1.07)^n\right]}

    Can you proceed?
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  3. #3
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    Quote Originally Posted by oryxncrake View Post
    Can you show me how to solve for n in the equation:

    60000= 38400(1.07)^n


    Thank you.
    Isolate the base and the exponent using division and then take the logarithm using the property ln(a^k) = k\, ln(a)

    Spoiler:

    1.07^n = \frac{60000}{38400} = \frac{25}{16} = (\frac{5}{4})^2

    That last part will make sense next step

    n\, ln(1.07) = 2\, ln(1.25)

    n = \frac{2ln(1.25)}{ln(1.07)} = 6.60 (3sf)
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  4. #4
    A riddle wrapped in an enigma
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    Another way...

    60000=38400(1.07^n)

    \frac{60000}{38400}=1.07^n

    1.07^n=\frac{25}{16}

    \ln 1.07^n=\ln \frac{25}{16}

    n \ln 1.07=\ln 25- \ln 16

    n=\frac{\ln25-\ln16}{\ln1.07}
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