Hello, karleewil!
I don't understand your steps . . .
Note that: .
We have: .
. .
Factor: .
The only acceptable root is: .
log(x-16)+log(x-64)=2
2=log 100 (base is 10)
therfor log(x-16)+log(x-64)=log(100)
recall that loga+logb=logab
therfor log((x-16)(x-64))=log100
or (x-16)(x-64)=100
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.