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Math Help - Easy exponential equation but don't know how to solve properly.

  1. #1
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    Easy exponential equation but don't know how to solve properly.

    Hi,

    I have this simple exponential equation:

    3^(x+2) + 3^(x-2) = 246

    It is easy to see that the sum must be 243 + 3 = 3^5 + 3^1 and therefore x = 3.
    But I haven't been able to solve it in the conventional way, using logarithms or some other method. Do you have any ideas to offer? Many thanks.
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  2. #2
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    Re: Easy exponential equation but don't know how to solve properly.

    Quote Originally Posted by freighter View Post
    Hi,

    I have this simple exponential equation:

    3^(x+2) + 3^(x-2) = 246

    It is easy to see that the sum must be 243 + 3 = 3^5 + 3^1 and therefore x = 3.
    But I haven't been able to solve it in the conventional way, using logarithms or some other method. Do you have any ideas to offer? Many thanks.
    9\cdot 3^x+\frac{1}{9} \cdot 3^x=246

    (9+\frac{1}{9})\cdot 3^x=246

    \frac{82}{9} \cdot 3^x=246

    3^x=27

    3^x=3^3

    x=3
    Thanks from freighter
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  3. #3
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    Re: Easy exponential equation but don't know how to solve properly.

    3^{x+2}+3^{x-2}=3^{x-2}(3^4+1)=3^{x-2}\cdot82=246.
    Thanks from freighter
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  4. #4
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    Re: Easy exponential equation but don't know how to solve properly.

    Thanks, it's clear for me now
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