Difference between revisions of "1950 AHSME Problems/Problem 18"
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Of the following | Of the following | ||
(1) <math> a(x-y)=ax-ay </math> | (1) <math> a(x-y)=ax-ay </math> | ||
| − | (2) <math> a | + | (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> | ||
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==Solution== | ==Solution== | ||
| − | The distributive property doesn't apply to logarithms in the ways illustrated, and only applies to addition and subtraction. | + | 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>\textbf{(E)} \text{Only 1 is true}</math> |
| − | |||
==See Also== | ==See Also== | ||
{{AHSME box|year=1950|num-b=17|num-a=19}} | {{AHSME box|year=1950|num-b=17|num-a=19}} | ||
Revision as of 11:35, 29 December 2011
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 AHSME (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 | ||
| All AHSME Problems and Solutions | ||
