Question

If 10^x equals 0.1 percent of 10^y, where x and y are integers, which of the following must be true?
a. y=x+2
b. y=x+3
c. x=y+3
d. y=1,000x
e. x=1,000y

Answer 1

$10^x=0.1 \% \times 10^y \\ \\ 10^x=\frac{0.1}{100} \times 10^y \\ \\ 10^x=\frac{1}{1000} \times 10^y \\ \\ 10^x=\frac{10^y}{10^3} \\ \\ 10^x=10^{y-3} \\ \\ \log_{10} 10^x=\log_{10} 10^{y-3} \\ \\ x=y-3 \\ \\ y=x+3$

The answer is B.