Question

Solve:
1.) 2 log 2 x - log 2 (x+3) = 2
2.)Solve: log 4 x = 1/2
3.)log b 9 = 2
4.)log 2 y = 1/3 (log 2 27)

Answer 1

1) log2x^2-log(2x+6)=2
log((2x^2)/(2x+6))=2
therfore 10^2=((2x^2)/2x+6))
100(2x+6)=2x^2
200x+600=2x^2
2x^2-200x-600=0
x^2-100x-300=0

then simplify using the quadratic equation .
which by my calculations should give x=102.9150262 or x=-2.915026221