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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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      Log On


   

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(39626) About Me  (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.
log%28b%2C%28x%5E2%2B3x-9%29%5E%282x-8%29%29=log%28b%2C1%29
%282x-8%29%2Alog%28b%2C%28x%5E2%2B3x-9%29%29=0
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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, highlight%28x=-4%29------that's one answer.
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Using log%28b%2C%28x%5E2%2B3x-9%29%29=0, and then translating into exponential form, you have
b%5E0=x%5E2%2B3x-9
1=x%5E2%2B3x-9
x%5E2%2B3x-10=0-----Factorable!!!
highlight_green%28%28x-2%29%28x%2B5%29=0%29
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ANSWER RESULTS:::::: highlight%28x=2%29 or highlight%28x=-5%29, or as also found highlight%28x=-4%29.
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Answer by MathTherapy(10556) About Me  (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)


highlight_green%28x+=+2%29,highlight_green%284%29, or highlight_green%28-+5%29

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