Question 573761: Please answer my question.
Kindly solve the equation and find the solution set.
log base of 3 (2x-3)+log base of 3 (x-4)=1
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! log base of 3 (2x-3)+log base of 3 (x-4)=1
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Since log a + log b = log(ab), we can combine the sum into a single logarithm:
log3((2x-3)(x-4)) = 1
Now get rid of the logarithm:
3^(log3((2x-3)(x-4)) = 3^1
(2x-3)(x-4) = 3
Multiply using FOIL and collect terms:
2x^2 - 11x + 9 = 0
Factor:
(2x-9)(x-1) = 0
This gives x=1, x=9/2
The 1st solution is disallowed, since this would result in the logarithm of a negative number
So the answer is x=9/2
Check:
log3((9-3)(9/2-8/2)) = log3(6*1/2) = log3(3) = 1
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