1950 AHSME Problems/Problem 18: Difference between revisions

Revision as of 10:58, 5 July 2013

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 $\textbf{(E)} \text{ Only 1 is true}$

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

Revision as of 18:47, 20 June 2012 view source 1=2 (talk \| contribs) 4,129 edits mNo edit summary ← Older edit		Revision as of 10:58, 5 July 2013 view source Nathan wailes (talk \| contribs) 2,960 edits No edit summary Newer edit →
Line 18:		Line 18:

	[[Category:Introductory Algebra Problems]]		[[Category:Introductory Algebra Problems]]
			{{MAA Notice}}

Page

Toolbox

Search

1950 AHSME Problems/Problem 18: Difference between revisions

Revision as of 10:58, 5 July 2013

Problem

Solution

See Also