Difference between revisions of "1950 AHSME Problems/Problem 18"
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Of the following | Of the following | ||
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(1) <math> a(x-y)=ax-ay </math> | (1) <math> a(x-y)=ax-ay </math> | ||
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(2) <math> a^{x-y}=a^x-a^y </math> | (2) <math> a^{x-y}=a^x-a^y </math> | ||
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(3) <math> \log (x-y)=\log x-\log y </math> | (3) <math> \log (x-y)=\log x-\log y </math> | ||
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(4) <math> \frac{\log x}{\log y}=\log{x}-\log{y} </math> | (4) <math> \frac{\log x}{\log y}=\log{x}-\log{y} </math> | ||
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(5) <math> a(xy)=ax\times ay </math> | (5) <math> a(xy)=ax\times ay </math> | ||
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<math> \textbf{(A)}\ \text{Only 1 and 4 are true}\qquad\\ \textbf{(B)}\ \text{Only 1 and 5 are true}\qquad\\ \textbf{(C)}\ \text{Only 1 and 3 are true}\qquad\\ \textbf{(D)}\ \text{Only 1 and 2 are true}\qquad\\ \textbf{(E)}\ \text{Only 1 is true} </math> | <math> \textbf{(A)}\ \text{Only 1 and 4 are true}\qquad\\ \textbf{(B)}\ \text{Only 1 and 5 are true}\qquad\\ \textbf{(C)}\ \text{Only 1 and 3 are true}\qquad\\ \textbf{(D)}\ \text{Only 1 and 2 are true}\qquad\\ \textbf{(E)}\ \text{Only 1 is true} </math> |
Revision as of 20:27, 27 January 2015
Problem
Of the following
(1)
(2)
(3)
(4)
(5)
Solution
The distributive property doesn't apply to logarithms or in the ways illustrated, and only applies to addition and subtraction. Also, , so
See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.