1964 AHSME Problems/Problem 1

Revision as of 03:05, 23 July 2019 by Talkinaway (talk | contribs) (See Also)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

What is the value of $[\log_{10}(5\log_{10}100)]^2$?

$\textbf{(A)}\ \log_{10}50 \qquad \textbf{(B)}\ 25\qquad \textbf{(C)}\ 10 \qquad \textbf{(D)}\ 2\qquad \textbf{(E)}\ 1$


Solution

$[\log_{10}(5\log_{10}100)]^2$

Since $10^2 = 100$, we have $\log_{10} 100 = 2$, so:

$[\log_{10}(5\cdot 2)]^2$

Multiply:

$[\log_{10}(10)]^2$

Since $10^1 = 10$, we have $\log_{10} 10 = 1$, so:

$[1]^2$

$1$

$\fbox{E}$.

See Also

1964 AHSC (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png