Question 605068
log base 3 (x+4)+log base 3 (x-2) = 3
Combine the logs
{{{log3((x+4)*(x-2)) = 3}}}
FOIL
{{{log3(x^2+2x-8) = 3}}}
the exponent equiv of logs
{{{x^2 + 2x - 8 = 3^3}}}
:
{{{x^2 + 2x - 8 = 27}}}
;
{{{x^2 + 2x - 8 - 27 = 0}}}
:
{{{x^2 + 2x - 35 = 0}}}
Factors to
(x+7)(x-5) = 0
Two solutions
x = -7
x = 5, since we are dealing with logs, only the positive solution is valid