Find the value of x for log 2 to the base x ×log 2 to the base x/16= log 2 to the base x/64

is X = 4??

We have : logx2 *logx/16 2=logx/64 2 Now we can write this as 1/log2x * 1/log2 x/16 = 1/log2 x/64 we get log2 x/64 = log2X * log2 x/16 Now we know that log(a/b) = log(a) - log(b) we get log2x-log2 64 = log2 x( log2 x-log2 16) log2X-6= log2X(log2X+4) Let log2X= P we get p-6=p^2-4p we get p^2-5p+6=0 p=3 and p=2 so log2x=3 and 2 we get x as 4 and 8