Question

log (base 2) X + log (base x) 2 = 2

Answer 1

$$\log_2 x +\log_x 2 = 2$$
Take both sides to the power of 2:
$$2^{\log_2 x + \log_x 2} = 4 \\
= 2^{\log_2 x} 2^{\log_x 2} = 4 \\
= x 2^{log_x 2} = 4$$
What do you think we can do now?

Answer 2

here is a hint. Let u = log(x), then you'll u/log2 + (log2)/u = 2, and x must be positive and not equal 1. You have a quadratic equation to solve.