Problem: If it is known that log2a+log2 b≦6 and that ab is a maximum, then the least value that can be taken on by a+b is:
Answer Choices:
A. 26
B. 6
C. 82
D. 16
E. none of these
Solution:
Since log2a+log2b≦6,log2ab≦6. ∴ab≦26=64. Since ab is a maximum, ab= 64. Therefore, the least value that can be taken on by a+b is 8+8=16. [ff P=ab,
the least value of a+b is P+P=2P. One way of proving this theorem is to consider the minimum value of f=a2−aS+P where S=a+b.
Hint.
S=a+b=a+aP.]