SOLUTION: please help me solve this
log (6x+5) - log (3) = log (2) - log (x)
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Question 241186: please help me solve this
log (6x+5) - log (3) = log (2) - log (x)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Presuming equal bases:
1. The sum of the logs is the log of the product.
2. The difference of the logs is the log of the quotient.
3. If the logs are equal, the arguments are equal.
\ +\ \log(3)\ =\ \log(2)\ -\ \log(x))
\ =\ \log\left(\frac{2}{x}\right))
Solve the quadratic. The quadratic does not factor over the rationals, so you will need to use the quadratic formula. (or complete the square, if you prefer -- though I would recommend against it in this case). You must then exclude any root that would cause either of the log arguments containing the variable to be negative.
John
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