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Math Help - how to solve 5^(x-1) 5^(x+2) = 10?

  1. #1
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    how to solve 5^(x-1) 5^(x+2) = 10?

    Hi,
    Can anyone tell me how to solve x for this equation: 5^(x-1) 5^(x+2) = 10?
    Thank you
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  2. #2
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    Quote Originally Posted by ycdfd View Post
    Hi,
    Can anyone tell me how to solve “x” for this equation: 5^(x-1) – 5^(x+2) = 10?
    Thank you
    5^{x-1} - 5^{x+2} = 10

    5^{x-1} - 5^{x-1}\times 5^{3} = 10

    5^{x-1} (1-125) = 10

    5^{x-1} = \frac{-10}{124}

    Since 5 ^{anything} \ne \text { a negative number}

    Thus x has no values
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  3. #3
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    Quote Originally Posted by ycdfd View Post
    Hi,
    Can anyone tell me how to solve “x” for this equation: 5^(x-1) – 5^(x+2) = 10?
    Thank you
    This equation doesn't have a real solution:

    \begin{aligned}5^{x-1}-5^{x+2}=&10 \\ \frac15 \cdot 5^x-25 \cdot 5^x = &10 \\ -\frac{124}5 \cdot 5^x =& 10\\5^x=&-\frac{50}{124}\end{aligned}

    A power with a positive base will never be negative.

    Thus x \notin \mathbb{R}
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