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Math Help - Solving Exponential Equations Using Logs

  1. #1
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    Solving Exponential Equations Using Logs

    Hello everyone.

    I was honing my skills at a variety of previous learned math operations and found one that I was unable to solve.

    125n^(x)=n^(x+3), n can not equal zero then 125n is equal to?

    From checking and guessing I was able to get n=5 then confirmed that with a graphing utility. Unfortunately, I always get stuck solving 125n^(x)=n^(x+3) algebraically using logs. Could someone walk me through the steps involved to isolate the variable n

    Thanks a lot.
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  2. #2
    MHF Contributor

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    Divide both sides by n^x!

    \frac{125n^x}{n^x}= \frac{n^{x+3}}{n^x}
    125= 5^3= n^3 which tells us that n= 5.

    With n= 5, your equation is true for all x. With n any number other than 5, it is false for all x.
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