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Thread: Solve equation for X: 125^(3x) = 1/5^(18) (so far, I have (125)^{3x} * 5^{18} = 1)

  1. #1
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    Solve equation for X: 125^(3x) = 1/5^(18) (so far, I have (125)^{3x} * 5^{18} = 1)

    Solve this equation for X

    1253x =1/518




    So far I have , (125)3x * 518 = 1

    What kind of steps are required here?

    Or I was thinking perhaps writing the expression as such

    1253x = 5-18

  2. #2
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    Quote Originally Posted by richiesmasher View Post
    1253x = 5-18
    Looks good. How do we get a simple equation from this?

  3. #3
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    Quote Originally Posted by richiesmasher View Post
    1253x = 5-18
    Hint: when you are solving exponential equations, it's a good idea to be familiar with powers of 2, 3, 4, 5 so you can recognize them when you see them. In particular, since one base is 5, it would be very nice if 125 was a power of 5, wouldn't it?

  4. #4
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    Quote Originally Posted by lev888 View Post
    Looks good. How do we get a simple equation from this?
    Got it:
    1253x =5-18

    = (53)3x= 5-18

    59x=5-18

    (because both bases are the same)

    9x=-18
    x= -2

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