Test 17
1.
\(\left.\begin{aligned}2^x=16\\2^y=32\end{aligned}\right\}\)
\(\Rightarrow\samefrac{x-y}{x+y}=?\)
A) \(-\samefrac{1}{18}\)B) \(-\samefrac{1}{9}\)C) \(\samefrac{1}{3}\)D) \(\samefrac{1}{9}\)E) \(\samefrac{1}{18}\)
2.
\(\left.\begin{aligned}9^x=125\\27^y=25\end{aligned}\right\}\)
\(\Rightarrow\samefrac xy=?\)
A) \(\samefrac{2}{3}\)B) \(\samefrac{3}{4}\)C) \(1\)D) \(\samefrac{4}{3}\)E) \(\samefrac{9}{4}\)
3.
\(\left.\begin{aligned}4^m=125\\5^n=16\end{aligned}\right\}\)
\(\Rightarrow m\cdot n=?\)
A) \(3\)B) \(4\)C) \(6\)D) \(8\)E) \(12\)
4.
\(x,z\in \mathbb{Z}^-\)
\(y\in \mathbb{Z}^+\)
\(x^y=4\)
\(x^z=\samefrac{1}{16}\)
\(\Rightarrow\samefrac{x+2y}{x-z}=?\)
A) \(-2\)B) \(-1\)C) \(0\)D) \(1\)E) \(2\)
5.
\(\left.\begin{aligned}x^a=9\\x^2=3\cdot x^{-b}\end{aligned}\right\}\)
\(\Rightarrow a=?\)
A) \(2b\)B) \(b\)C) \(b+1\)D) \(2b+2\)E) \(2b+4\)
6.
\(\left.\begin{aligned}2^x\cdot3^y=18\\3^x\cdot2^y=72\end{aligned}\right\}\)
\(\Rightarrow x+y=?\)
A) \(2\)B) \(3\)C) \(4\)D) \(5\)E) \(6\)
7.
\(\left.\begin{aligned}2^{a+3}\cdot5^b=400\\2^b\cdot5^{a+3}=2500\end{aligned}\right\}\)
\(\Rightarrow a+b=?\)
A) \(3\)B) \(5\)C) \(6\)D) \(9\)E) \(11\)
8.
\(\left.\begin{aligned}3^x\cdot5^y=9\\3^y\cdot5^x=25\end{aligned}\right\}\)
\(\Rightarrow x-y=?\)
A) \(-2\)B) \(-1\)C) \(0\)D) \(1\)E) \(2\)