Question 409919: Solve for x.
log3(x+7)=2-log3(x-1)
Write the exact answer using base-10 logarithms.
log3(x+7)=2-log3(x-1)
log3(x+7) + log3(x-1) = 2
log3 [(x+7)/(x-1)] = 2
(x+7)(x-1) = 3^2
x^2 + 6x - 7 = 9
x^2 + 6x - 16 = 0
(x+8)(x-2) = 0
x = -8 or x = 2
but x=-8 would make log3(x+7) undefined, so
x = 2
( why would it ask to use base 10 logs ????)
You can put this solution on YOUR website! You've done the problem perfectly. I can only guess that the instruction regarding base 10 logarithms applies to a set of problems, some of which may require logarithms to solve.
(