SOLUTION: is 6.5 a solution of log base 3 of (x + 3) + log base 3 of (x-2) = log base 3 of 14 and please show your work?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: is 6.5 a solution of log base 3 of (x + 3) + log base 3 of (x-2) = log base 3 of 14 and please show your work?      Log On


   

Question 454532: is 6.5 a solution of log base 3 of (x + 3) + log base 3 of (x-2) = log base 3 of 14 and please show your work?
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
log%283%2C+%28x%2B3%29%29%2Blog%283%2C+%28x-2%29%29=log%283%2C+14%29, using log properties we get:
log%283%2C+%28x%2B3%29%28x-2%29%29=log%283%2C+14%29=>%28x%2B3%29%28x-2%29=14, we solve now the
quadratic equation:x%5E2%2Bx-20=0, by factoring %28x%2B5%29%28x-4%29=0 and get:
x=-5 and x=4. We reject the root x=-5, because the log of negative numbers are
undefined.
Answer: The solution is x=4.