Question

solve for x
log(2)(x-2)-4=-log(2)(x+4)

Answer 1

\[ x = -{\frac {\ln \left( 2 \right) -2}{\ln \left( 2 \right) }} \]

Answer 2

maybe try
\[\log_2(x-2)+\log_2(x+4)=4\] so
\[\log_2((x-2)(x+4))=4\] and then
\[(x-2)(x+4)=2^4\]

Answer 3

\[x^2+2x-8=16\]
\[x^2+2x=24\]
\[(x+1)^2=25\]
\[x+1=5\]
\[x=4\]

Answer 4

you may notice that i ignored
\[x+1=-5\]
\[x=-6\] because you cannot take the log of a negative number. also if completing the square is annoying you can write
\[x^2+2x-24=8\] and factor as
\[(x-4)(x+6)=0\] etc