Question 324536: How do you solve log25(x-1)+log25(x+3)=1/2
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
\ +\ \log_{25}\left(x\ +\ 3\right)\ =\ \frac{1}{2})
First use: The sum of the logs is the log of the product, that is:
 + \log_b(y) = \log_b(xy))
(x\ +\ 3)\right)\ =\ \frac{1}{2})
\right)\ =\ \frac{1}{2})
Then use the definition of a logarithm:
 \ \ \Rightarrow\ \ b^y = x)
Which factors tidily. You will, as is usual with a quadratic equation, get 2 roots. However, in this case, and any time you are solving problems where you start out with functions, such as logarithms, that have restricted domains, you MUST check BOTH answers. It is possible that the original equation will have 2, 1, or 0 valid answers. Remember that the argument of the logarithm function, regardless of the base, must be strictly greater than zero.
John
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