Question

Find value of x for log1/2(x-1)+log1/2(x+1)-log1/√2(7-x)=1

Answer 1

log1/2(x-1)+log1/2(x+1)-log1/√2(7-x)=1

You seriously need to learn how to use parentheses. Also, the final result will depend on the base of the logarithms. I shall assume base 10.

Assuming you meant

log(1/(2(x-1)))+log(1/(2(x+1)))-log(1/(√2(7-x)))=1

log (1/(2(x-1)) * 1/(2(x+1)) * √2(7-x)) = 1

1/(2(x-1)) * 1/(2(x+1)) * √2(7-x) = 10

I'll let you solve the cubic in any way you like, but somehow I feel the question has been garbled.

I suggest you type in your equation at wolframalpha.com and see how it interprets your text. Then use enough parentheses to make it come out right.