Problem: For all positive numbers x distinct from 1,
log3​x1​+log4​x1​+log5​x1​
equals
Answer Choices:
A. log60​x1​
B. logx​601​
C. (log3​x)(log4​x)(log5​x)1​
D. (log3​x)+(log4​x)+(log5​x)12​
E. (log3​x)(log5​x)log2​x​+(log2​x)(log5​x)log3​x​+(log2​x)(log3​x)log5​x​
Solution:
If y=loga​b, then ay=b and a=b1/y. Thus
logb​a=y1​=loga​b1​
Thereiore,
​log3​x1​+log4​x1​+log5​x1​=logx​3+logx​4+logx​5=logx​60=log60​xi​.​