I don't understand your steps . . .
Note that: .
We have: .
The only acceptable root is: .
2=log 100 (base is 10)
recall that loga+logb=logab
by solving them you will get x=14 and x=66
we will neglect x=14 as it do not satisfy the domain of given equation(it makes log negative i.e log(-2) and log (-50))
so the final answer is x=66
You could use the quadratic formula here, but this shouldn't be too difficult to factor. We want to find two numbers whose product is 924 and whose sum is -80. Our possible integer factorizations of 924 are (plus or minus) and . Of these choices, only -14 and -66 work. So we get
Note, however, that 14 is not a valid solution, since is not defined over the reals. Thus is the only solution.