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:

$\log 17$

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

$\log 15$

$\log 600$

$\log 0.4$

Answer: A

Concepts:logarithm prime factorization

Difficulty rating: 1470

Small Hint:

The two given values determine $\log2$ and $\log3$

Big Hint:

Use $\log5=1-\log2$ , then see which choice has a prime factor other than $2,3,5$

Solution:

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.

1951 AMC 12 Problem 45

Answer: A

Difficulty rating: 1470

Small Hint:

Big Hint:

Solution:

Problem 45 in Other Years