solve equation log2x + logx2=2.5
First change the base on logx2 using the change of base identity:
Then your equation becomes
log2x + 1/log2x =2.5
Let u=log2x and simplify:
Use the quadratic formula to solve this quadratic equation, get u = 2 or 1/2.
For u=2=log2x, x=4.
For u=1/2=log2x, x=√2
Therefore, the two solutions are x=4 and x=√2
Check: log24 + log42 = 2+1/2=2.5
log2√2 + log √22 = 1/2 + 2 =2.5