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Math Help - Need help finding out what the variable x is equal to in this exponential decay eq.

  1. #1
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    Question Need help finding out what the variable x is equal to in this exponential decay eq.

    (√5 / 25) = 53-x

    How do you find the value of x? My calculator says that x is equal to 4.5. However, can someone please show me the work to finding the answer to this equation? Thanks!
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    Re: Need help finding out what the variable x is equal to in this exponential decay e

    Hey sameeranand21.

    Are you familiar with logarithms in arbitrary bases?

    SQRT(5)/25 = SQRT(5)/[SQRT(5)*5*SQRT(5)] = 1/[5*SQRT(5)] = 5^(-3/2) = 5^(3-x).

    So you can use logarithms or use the fact that if 5^x = 5^y then x = y (also known as injective property of function).
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    Re: Need help finding out what the variable x is equal to in this exponential decay e

    I am not understanding how you found this: SQRT(5)/25 = SQRT(5)/[SQRT(5)*5*SQRT(5)]

    Nor am I understanding how this 1/[5*SQRT(5)] equals this 5^(-3/2).
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    Re: Need help finding out what the variable x is equal to in this exponential decay e

    1/a^x = a^(-x) and a^(x)*a^(y) = a^(x+y).

    SQRT(5) = 5^(1/2) 5*SQRT(5) = 5^(1+1/2) = 5^(3/2)

    1/5^(3/2) = 5^(-3/2)
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