pre-cal: one-to-one property

i am not sure how to do these problems...

*use the one-to-one property to solve the equation for x*

1. 2^(x-2)= 1/32
2. e^(x^2-3)=e^2x

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  1. I have no idea what the one-on-one property is.

    Both of these log equations can be solved by taking the log of each side

    1- take log2 of each side,
    x-2=-5

    2- take ln of each side
    x^2-3=2x

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    bobpursley
  2. the 1-1 property states that if the bases are equal the exponents are equal. therefore u must set 1/32 as 2^1/5. then 2^(x-2)= 2^(1/5) and then x-2=1/5. x=11/5

    for 2), same thing. x^2 - 3= 2x.
    x^2 - 2x - 3 = 0 (x-3)(x+1) = 0 x=3,-1.

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  3. how to solve 5^x-2 = 1/125

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  4. e^(X^2+6)=e^5X

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