[log (X)]^2=2logx +3

Question

the log(X) term  on the left side of the equation is squared. How do you do that?

Answer 1

Let y=logx, then y^2-2y-3=0, which factorises: (y-3)(y+1)=0. So y=3 or -1. That means logx=3 or -1 and (for log to base 10) x=1000 or 0.1. To any other base, b, x=b^3 or 1/b. Substitute these values of x in the original equation to check out the answer: (x=b^3) 9=6+3 and (x=1/b) 1=-2+3. Correct!