1950 AHSME Problems/Problem 18

Problem

Of the following (1) $a(x-y)=ax-ay$ (2) $a(x-y)=ax-ay$ (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 in the ways illustrated, and only applies to addition and subtraction. Therefore $\boxed{\mathrm{(D)}\text{ only }1\text{ and }2\text{ are true.}}$

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
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1950 AHSME Problems/Problem 18

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