Log4 (x+1) + log4 (x-2) =1
This is not a calculator problem. Use the rules you have learned to simplify your problem.
For a a log in any base. log(a*b) =log(a) +log(b) or log(a)+log(b) =log(a*b).
Use the fact that log4=log in base 4 and rewrite the equation with the appropriate symbols. log4[(x+1)*(x-2)] =1
However 1=log4(4) and
The equality of the two logs implies the equality of their arguments (contents) and
Now you solve this quadratic equation by the methods you must have learned (sorry I have to leave some thing for you to do, to ensure that proper learning is achieved).
Once you find the roots of the quadratic equation, verify that each term in your original expression has meaning-- x+1 positive and x-2 positive.
If one of the roots makes the argument (x+1) or (x-2) negative, reject it. because the argument of a log function cannot be negative.
Dec 14, 2009 |
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