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Thread: Solving Exponential Functions

  1. February 20th 2008, 12:11 PM #1
    onenameless
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    Solving Exponential Functions

    I know several methods in finding the value o x, but i can't figure this one out:

    5^(x+2) - 5^(x) = 24

    So that says 5 to the power of x plus 2 minus 5 to the power of x equals 24.
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  2. February 20th 2008, 12:33 PM #2
    Soroban
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    Hello, onenameless!

    Solve for x\!:\;\;5^{x+2} - 5^x \:= \:24

    We have: . 5^2\!\cdot\!5^x - 5^x \:=\:24

    Factor: . (5^2-1)\!\cdot\!5^x\:=\:24\quad\Rightarrow\quad 24\cdot5^x\:=\:24 \quad\Rightarrow\quad 5^x \:=\:1

    Therefore: . x \:=\:0
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