Question

Solve the logarithmic equation. Please show all of your work. log6(x+2)+log6(x-3)=1

Answer 1

\[\log_{6}(x+2)(x-3)=1 \]

Answer 2

\[6^{1}=(x+2)(x-3)\]

Answer 3

\[x^2-x-6=6\]

Answer 4

log6(x+2)+log6(x-3) = 1
by laws of logs
log6 (x+2(x-3) = 1
(x+2)(x-3) = 6
x^2 -x - 6 = 6
x^2 - x -12 = 0
(x-4)(x+3) = 0
x = 4 or -3