SOLUTION: Solve the logarithmic equation: Log base 4(2x+1)= Log base 4(x-3) + Log base 4(x+5)

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Question 193996: Solve the logarithmic equation:
Log base 4(2x+1)= Log base 4(x-3) + Log base 4(x+5)
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




The sum of the logs is the log of the product, so:



If two logs to the same base are equal, then their arguments must be equal, so:











or



But if then , and the domain of the log function is . Hence, you must exclude , and the solution set for the given equation is

Check:






But , so:

Checks.

John