SOLUTION: Question: Determine the values of "x" that satisfy the equation (x^2+3x-9)^(2x-8)=1 I'm getting stuck because there's a variable in both the coefficient and the argument when co

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Question 856416: Question: Determine the values of "x" that satisfy the equation (x^2+3x-9)^(2x-8)=1
I'm getting stuck because there's a variable in both the coefficient and the argument when converted to log form.
This is what I have so far:

1.(2x-8)log(x^2+3x-9)=log1
2. 2xlog(x^2+3x-9)-8log(x^2+3x-9)=log1
3. 2xlog(x^2+3x-9)=8log(x^2+3x-9)+log1
4. xlog(x^2+3x-9)=(8log(x^2+3x-9)(1)/2)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39628)   (Show Source): You can put this solution on YOUR website!
Logarithms of both sides should be equal, no matter the base of the logarithm taken.


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The easier answer to find is to allow 2x-8=0, because either one factor OR the other must be zero. Continuing with this factor, ------that's one answer.
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Using , and then translating into exponential form, you have


-----Factorable!!!

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ANSWER RESULTS:::::: or , or as also found .
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Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!

Question: Determine the values of "x" that satisfy the equation (x^2+3x-9)^(2x-8)=1
I'm getting stuck because there's a variable in both the coefficient and the argument when converted to log form.
This is what I have so far:

1.(2x-8)log(x^2+3x-9)=log1
2. 2xlog(x^2+3x-9)-8log(x^2+3x-9)=log1
3. 2xlog(x^2+3x-9)=8log(x^2+3x-9)+log1
4. xlog(x^2+3x-9)=(8log(x^2+3x-9)(1)/2)


,, or 

=============

You can do the check!! 

If you need a complete and detailed solution, let me know!!



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