Problem:
If b>1,x>0 and (2x)logb2−(3x)logb3=0, then x is
Answer Choices:
A. 2161
B. 61
C. 1
D. 6
E. not uniquely determined
Solution:
For this solution write log for logb. The given equation is equivalent to
(2x)log23log32log23log3−2log2=(3x)log3=xlog2xlog3=xlog3−log2
Equating the logarithm of the left and right members of the last equality above yields
(log2)2−(log3)2−(log2+log3)log6161=(log3−log2)logx=logx=logx=x.