Ordering of the expressions below.
1.
\(a=5^2\)
\(b=5^4\)
\(c=5^8\)
2.
\(a=(-3)^2\)
\(b=(-3)^4\)
\(c=(-3)^5\)
3.
\(a=2^{-7}\)
\(b=2^5\)
\(c=2^{-3}\)
4.
\(a=(-4)^{-2}\)
\(b=(-4)^2\)
\(c=(-4)^3\)
5.
\(a=\left(\samefrac{2}{7}\right)^{-1}\)
\(b=\left(\samefrac{2}{7}\right)^2\)
\(c=\left(\samefrac{2}{7}\right)^5\)
6.
\(a=\left(\samefrac{1}{6}\right)^{-3}\)
\(b=\left(\samefrac{1}{6}\right)^{-5}\)
\(c=\left(\samefrac{1}{6}\right)^{-10}\)
7.
\(a=3^{30}\)
\(b=3^{45}\)
\(c=3^{75}\)
8.
\(a=(2^3)^5\)
\(b=2^{(2^3)}\)
\(c=(2^3)^{12}\)
9.
\(a=2^{60}\)
\(b=3^{80}\)
\(c=5^{40}\)
10.
\(2^a=17\)
\(3^b=12\)
\(5^c=138\)
11.
\(4^a=67\)
\(5^b=30\)
\(7^c=14\)
12.
\(15^{3x-1}=230\)
\(\to ?<x<?\)
13.
\(a\in \mathbb{Z}^+\)
\(\left(\samefrac{4}{7}\right)^{2a+5}<\left(\samefrac{4}{7}\right)^{17-a}\)
\(\Rightarrow\min(a)=?\)
14.
\(a\in \mathbb{Z}\)
\(\left(\samefrac{1}{3}\right)^{3a-7}<3^{a-9}\)
\(\Rightarrow\min(a)=?\)
15.
\(a\in \mathbb{Z}^-\)
\(\left(\samefrac{2}{5}\right)^{4-a}>\left(\samefrac{25}{4}\right)^{a+4}\)
\(\Rightarrow\max(a)=?\)
16.
\(a\in \mathbb{Z}\)
\(8^{a+2}<2^{2a+13}\)
\(\Rightarrow\max(a)=?\)