1963 AHSME Problems/Problem 5

Problem

If $x$ and $\log_{10} x$ are real numbers and $\log_{10} x<0$ , then:

$\textbf{(A)}\ x<0 \qquad \textbf{(B)}\ -1<x<1 \qquad \textbf{(C)}\ 0<x\le 1 \\ \textbf{(D)}\ -1<x<0 \qquad \textbf{(E)}\ 0<x<1$

Solution

Let $\log_{10} x = a$ , so $10^a = x$ . Note that $10^0 = 1$ and that $10^a$ increases as $a$ increases. Since $a < 0$ , $10^a < 1$ . However, for all $a$ , $10^a > 0$ , so $0 < x < 1$ . The answer is $\boxed{\textbf{(E)}}$ .

1963 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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
All AHSME Problems and Solutions

Page

Toolbox

Search

1963 AHSME Problems/Problem 5

Problem

Solution

See Also