SOLUTION: solve 3 exponent x+3=9 exponent x for x

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Question 1078842: solve 3 exponent x+3=9 exponent x for x
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
solve 3 exponent x+3=9 exponent x for x
Assume the problem is:
3%5E%28%28x%2B3%29%29+=+9%5Ex
Raise both sides with the exponent 1%2Fx
:
3%5E%28%28x%2B3%29%2Fx%29+=+9%5E1, the first exponent is %28%28x%2B3%29%2Fx%29
Using nat logs
ln%283%5E%28%28x%2B3%29%2Fx%29%29+=+ln%289%29,
the log equiv of exponents
%28%28x%2B3%29%2Fx%29ln%283%29+=+ln%289%29
%28%28x%2B3%29%2Fx%29+=+ln%289%29%2Fln%283%29
ln of this fraction = 2
%28%28x%2B3%29%2Fx%29+=+2
x + 3 = 2x
3 = 2x - x
x = 3
;
:
See if that checks out using your calc
3^(3+3) = 3^6 = 729
9^3 = 729

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
solve 3 exponent x+3=9 exponent x for x
Use PARENTHESES next time. If 3%5E%28x+%2B+3%29+=+9%5Ex, then:

3%5E%28x+%2B+3%29+=+%283%5E2%29%5Ex

3%5E%28x+%2B+3%29+=+3%5E%282x%29

x + 3 = 2x ------ Bases are equal and so are the exponents



That's all.....nothing COMPLEX or CONFUSING!