Difference between revisions of "1950 AHSME Problems/Problem 18"

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==See Also==
 
==See Also==
  
{{AHSME box|year=1950|num-b=17|num-a=19}}
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{{AHSME 50p box|year=1950|num-b=17|num-a=19}}
  
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]

Revision as of 07:33, 29 April 2012

Problem

Of the following (1) $a(x-y)=ax-ay$ (2) $a^{x-y}=a^x-a^y$ (3) $\log (x-y)=\log x-\log y$ (4) $\frac{\log x}{\log y}=\log{x}-\log{y}$ (5) $a(xy)=ax\times ay$

$\textbf{(A)}\ \text{Only 1 and 4 are true}\qquad\\ \textbf{(B)}\ \text{Only 1 and 5 are true}\qquad\\ \textbf{(C)}\ \text{Only 1 and 3 are true}\qquad\\ \textbf{(D)}\ \text{Only 1 and 2 are true}\qquad\\ \textbf{(E)}\ \text{Only 1 is true}$

Solution

The distributive property doesn't apply to logarithms or in the ways illustrated, and only applies to addition and subtraction. Also, $a^{x-y} = \frac{a^x}{a^y}$, so $\textbf{(E)} \text{Only 1 is true}$

See Also

1950 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 17
Followed by
Problem 19
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