Difference between revisions of "1950 AHSME Problems/Problem 18"
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− | == Problem== | + | == Problem == |
+ | Of the following | ||
− | |||
(1) <math> a(x-y)=ax-ay </math> | (1) <math> a(x-y)=ax-ay </math> | ||
+ | |||
(2) <math> a^{x-y}=a^x-a^y </math> | (2) <math> a^{x-y}=a^x-a^y </math> | ||
+ | |||
(3) <math> \log (x-y)=\log x-\log y </math> | (3) <math> \log (x-y)=\log x-\log y </math> | ||
+ | |||
(4) <math> \frac{\log x}{\log y}=\log{x}-\log{y} </math> | (4) <math> \frac{\log x}{\log y}=\log{x}-\log{y} </math> | ||
+ | |||
(5) <math> a(xy)=ax\times ay </math> | (5) <math> a(xy)=ax\times ay </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> | <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> | ||
− | ==Solution== | + | == Solution == |
+ | The distributive property doesn't apply to logarithms or in the ways illustrated, and only applies to addition and subtraction. Also, <math>a^{x-y} = \frac{a^x}{a^y}</math>, so <math>\boxed{\textbf{(E)} \text{ Only 1 is true}}</math>. | ||
− | + | == See Also == | |
− | ==See Also== | ||
{{AHSME 50p box|year=1950|num-b=17|num-a=19}} | {{AHSME 50p box|year=1950|num-b=17|num-a=19}} | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
+ | {{MAA Notice}} |
Revision as of 00:52, 12 October 2020
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 | |
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All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.