Problem:
What is the value of a for which log2​a1​+log3​a1​+log4​a1​=1 ?
Answer Choices:
A. 9
B. 12
C. 18
D. 24
E. 36
Solution:
By the change of base formula, logm​n1​=logn​m. Thus
1=log2​a1​+log3​a1​+log4​a1​=loga​2+loga​3+loga​4=loga​24
It follows that a=24​.
The problems on this page are the property of the MAA's American Mathematics Competitions