Problem: If you are given log8=.9031 and log9=.9542, then the only logarithm that cannot be found without the use of tables is:
Answer Choices:
A. log17
B. log45
C. log15
D. log600
E. log.4
Solution:
log8=log23=3log2;log9=log32=2log3;log10=1 and log5=log(10/2)=log10−log2=1−log2. From these and from the information supplied in the problem,
log2=31log8,log3=21log9, and log5=1−log2
can be found; consequently, so can the logarithm of any number representable as a product of powers of 2,3 and 5. Since 17 is the only number in the list not representable in this way, (A) is the correct choice.