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Math Help - logarithm #3

  1. #1
    Newbie Zharif93's Avatar
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    logarithm #3

    3 ^ ( x+3 ) - 3 ^ ( x+2 ) = 2
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  2. #2
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    Quote Originally Posted by Zharif93 View Post
    3 ^ ( x+3 ) - 3 ^ ( x+2 ) = 2
    By inspection (or simply by intelligent trial-and-error) x = -2. That is the technique you would be expected to use if access to technology was not an option.
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  3. #3
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    3^{x+ 3}= 3^x3^3= 27(3^x). 3^{x+ 2}= 3^x3^2= 9(3^x).
    Your equation is the same as 27(3^x)- 9(3^x)= (27- 9)3^x= 18(3^x)= 2 so 3^x= \frac{2}{18}= \frac{1}{9}= 3^{-2}.

    I've always wondered about the phrase "using technology". It require technology to make a pencil doesn't it?
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  4. #4
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    3^{x+3}-3^{x+2}=3^{x+2}\left( 3-1 \right)=2, that's all.
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