Difference between revisions of "1964 AHSME Problems/Problem 1"

Revision as of 02:04, 23 July 2019

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

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

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

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:

$[1]^2$

$1$

$\fbox{E}$ .

1964 AHSC (Problems • Answer Key • Resources)
Preceded by First Problem	Followed by Problem 3
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

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-We do some simple logarithms here:
+==Problem==
-<math>[\log_{10}(5\log_{10}100)]^2 = [\log_{10}(5\cdot 2)]^2 = [\log_{10}(10)]^2 = [1]^2 = 1 \rightarrow \fbox{E}</math>.
+What is the value of <math>[\log_{10}(5\log_{10}100)]^2</math>?
+<math>\textbf{(A)}\ \log_{10}50 \qquad
+\textbf{(B)}\ 25\qquad
+\textbf{(C)}\ 10 \qquad
+\textbf{(D)}\ 2\qquad
+\textbf{(E)}\ 1  </math>
+==Solution==
+<math>[\log_{10}(5\log_{10}100)]^2</math>
+Since <math>10^2 = 100</math>, we have <math>\log_{10} 100 = 2</math>, so:
+<math>[\log_{10}(5\cdot 2)]^2</math>
+Multiply:
+<math>[\log_{10}(10)]^2</math>
+Since <math>10^1 = 10</math>, we have <math>\log_{10} 10 = 1</math>, so:
+<math>[1]^2</math>
+<math>1</math>
+<math>\fbox{E}</math>.
+==See Also==
+{{AHSME 40p box|year=1964|before=First Problem|num-a=3}}
+[[Category:Introductory Algebra Problems]]
+{{MAA Notice}}