Problem: If logb2​x+logx2​b=1,b>0,bî€ =1,xî€ =1, then x equals:
Answer Choices:
A. 1/b2
B. 1/b
C. b2
D. b
E. b​
Solution:
Let logb​x=m and let logx​2b=n. Then x=b2m and b=x2n.
∴(x2n)2 m=b2 m∴x4mn=x∴4mn=1∴n=4 m1​
∴m+4m1​=1∴m=21​∴x=b