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) (Show Source): You can put this solution on YOUR website!
} = \log_4{(x-3)} + \log_4{(x+5)})
The sum of the logs is the log of the product, so:
} = \log_4{\left\{(x-3)(x+5)\right\}})
If two logs to the same base are equal, then their arguments must be equal, so:
(x+5))
(x + 4) = 0)
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:
+1)} =^? \log_4{((4)-3)} + \log_4{((4)+5)})
} =^? \log_4{(1)} + \log_4{(9)})
But } = 0\ \ \forall\ b \geq 0)
, so:
} = \log_4{(9)})
Checks.
John
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