SOLUTION: Solve for x: 2logbase4(2x)-logbase4(3x-5)=logbase3 (9)???

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Question 132616: Solve for x:
2logbase4(2x)-logbase4(3x-5)=logbase3 (9)???
Answer by mathispowerful(115) About Me  (Show Source):
You can put this solution on YOUR website!
2log4%282x%29-log4%283x-5%29=log3%289%29
Solution:
Rewrite the equation:
log4%282x%29%5E2-log4%283x-5%29=log3%283%29%5E2
log4%28%282x%29%5E2%2F%283x-5%29%29=2log3%283%29
log4%28%282x%29%5E2%2F%283x-5%29%29=2
Replace 2 by log4%2816%29 since they are equal and we need base 4 log.
So we get
log4%28%282x%29%5E2%2F%283x-5%29%29=log4%2816%29
Compare the two sides, we get
%282x%29%5E2%2F%283x-5%29=16
Then multiply 3x-5 on both sides:
%282x%29%5E2=16%283x-5%29
4x%5E2=16%283x-5%29
divide by 4 on both sides:
x%5E2=4%283x-5%29
expand it and write into standard form:
x%5E2-12x%2B20=0
Factor left side:
(x-10)(x-2)=0;

So x=10 or x=2.
That's it!