Problem: The product, loga​b⋅logb​a is equal to:
Answer Choices:
A. 1
B. a
C. b
D. ab
E. none of these
Solution:
For permissible values of a and b,loga​b⋅logb​a≡1;
or
Let x=loga​b and y=logb​a.∴ax=b and by=a.
∴axy=by=a;∴xy=1;∴loga​b⋅logb​a=1.