1951 AMC 12 Problem 45

Question

If you are given

\log 8=0.9031

and

\log 9=0.9542,

then the only logarithm that cannot be found without the use of tables is:

\log 17

\log(\frac{5}{4})

\log 15

\log 600

\log 0.4

The two given values determine

\log2

and

\log3

Use

\log5=1-\log2

, then see which choice has a prime factor other than

2,3,5

From the data,

\begin{gathered} \log2=\frac13\log8,\\ \log3=\frac12\log9, \end{gathered}

and

\log5=1-\log2.

Therefore logarithms of products and quotients of powers of

2,3,5

can be computed. The number

17

has none of those prime factors, so its logarithm is not determined by the data.

Thus, the correct answer is A.

Problem 45 in other years