Difference between revisions of "1964 AHSME Problems/Problem 1"
Crocodile 40 (talk | contribs) (Created page with "We do some simple logarithms here: <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>.") |
Talkinaway (talk | contribs) |
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− | + | ==Problem== | |
− | <math>[\log_{10}(5\log_{10}100)]^2 = [\log_{10}(5\cdot 2)]^2 | + | 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}} |
Revision as of 02:04, 23 July 2019
Problem
What is the value of ?
Solution
Since , we have , so:
Multiply:
Since , we have , so:
.
See Also
1964 AHSC (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 3 | |
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All AHSME Problems and Solutions |
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