Exemplary Question Types
9.
\(3^x=a\)
\(2^x=b\)
What is the value of \(108^x\) in terms of a and b?
10.
\(m,n\in \mathbb{Z}\)
\(\left(\samefrac{1}{m}\right)^{-n}=\samefrac{1}{81}\)
\(\Rightarrow\min(m+n)=?\)
11.
\(x=9\cdot10^{-5}\)
\(\Rightarrow(0{,}03)\cdot(0{,}0003)\cdot(0{,}009)=?\)
12.
\(3^x\cdot5^y\cdot7^z=9\)
\(6^x\cdot10^y\cdot14^z=144\)
\(\Rightarrow x+y+z=?\)
13.
\(x^x+x^x+x^x+x^x=2^{26}\)
\(\Rightarrow x=?\)
14.
\(x=5^a-5^{-a}\)
\(y=5^a+5^{-a}\)
\(\Rightarrow y^2-x^2=?\)
15.
\(x^a\in \mathbb{R}^+\)
\(x^b\in \mathbb{R}^+\)
\(x^{a+b}=9\)
\(x^{a-b}=4\)
\(\Rightarrow x^a+x^b=?\)
16.
\((x-3)^{(x-5)}+3=x\)
\(\Rightarrow \text{S.S.}=?\)