\(1,4^x=8^4\\ \Rightarrow\left(2^2\right)^x=\left(2^3\right)^4\\ \Rightarrow2^{2x}=2^{12}\\ \Rightarrow2x=12\\ \Rightarrow x=\dfrac{12}{2}\\ \Rightarrow x=6\\ 2,4^x=32^{24}\\ \Rightarrow\left(2^2\right)^x=\left(2^5\right)^{24}\\ \Rightarrow2^{2x}=2^{120}\\ \Rightarrow2x=120\\ \Rightarrow x=\dfrac{120}{2}\\ \Rightarrow x=60\\ 3,8^x=16^{12}\\ \Rightarrow\left(2^3\right)^x=\left(2^4\right)^{12}\\ \Rightarrow2^{3x}=2^{48}\\ \Rightarrow3x=48\\ \Rightarrow x=\dfrac{48}{3}\\ \Rightarrow x=16\\ 4,4^x=8^{12}\\ \Rightarrow\left(2^2\right)^x=\left(2^3\right)^{12}\\ \Rightarrow2^{2x}=2^{36}\\ \Rightarrow2x=36\\ \Rightarrow x=\dfrac{36}{2}\\ \Rightarrow x=18\\ 5,4^x=32^{40}\\ \Rightarrow\left(2^2\right)^x=\left(2^5\right)^{40}\\ \Rightarrow2^{2x}=2^{200}\\ \Rightarrow2x=200\\ \Rightarrow x=\dfrac{200}{2}\\ \Rightarrow x=100\\ 6,8^x=32^9\\ \Rightarrow\left(2^3\right)^x=\left(2^5\right)^9\\ \Rightarrow2^{3x}=2^{45}\\ \Rightarrow3x=45\\ \Rightarrow x=\dfrac{45}{3}\\ \Rightarrow x=15\)
7: \(8^x=16^{99}\)
=>\(\left(2^3\right)^x=\left(2^4\right)^{99}\)
=>\(2^{3x}=2^{396}\)
=>3x=396
=>x=132
8: \(8^x=32^{33}\)
=>\(\left(2^3\right)^x=\left(2^5\right)^{33}\)
=>\(2^{3x}=2^{165}\)
=>3x=165
=>x=55
9: \(8^x=32^{66}\)
=>\(\left(2^3\right)^x=\left(2^5\right)^{66}\)
=>\(2^{3x}=2^{5\cdot66}=2^{330}\)
=>3x=330
=>x=110
10: \(16^x=32^8\)
=>\(\left(2^4\right)^x=\left(2^5\right)^8\)
=>\(2^{4x}=2^{40}\)
=>4x=40
=>x=10
11: \(32^x=16^{10}\)
=>\(\left(2^5\right)^x=\left(2^4\right)^{10}\)
=>5x=40
=>x=8
12: \(16^x=64^{10}\)
=>\(\left(4^2\right)^x=\left(4^3\right)^{10}\)
=>\(4^{2x}=4^{30}\)
=>2x=30
=>x=15
13: \(10000^x=1000^{24}\)
=>\(10^{4x}=\left(10^3\right)^{24}=10^{72}\)
=>4x=72
=>x=18
14: \(\left(\dfrac{1}{4}\right)^x=\left(\dfrac{1}{8}\right)^6\)
=>\(\left(\dfrac{1}{2}\right)^{2x}=\left(\dfrac{1}{2}\right)^{18}\)
=>2x=18
=>\(x=\dfrac{18}{2}=9\)
15: \(\left(\dfrac{1}{8}\right)^x=\left(\dfrac{1}{4}\right)^6\)
=>\(\left[\left(\dfrac{1}{2}\right)^3\right]^x=\left[\left(\dfrac{1}{2}\right)^2\right]^6\)
=>\(3x=2\cdot6=12\)
=>x=4
16: \(\left(\dfrac{1}{16}\right)^x=\left(\dfrac{1}{8}\right)^6\)
=>\(\left(\dfrac{1}{2}\right)^{4x}=\left(\dfrac{1}{2}\right)^{18}\)
=>4x=18
=>\(x=\dfrac{18}{4}=\dfrac{9}{2}\)
17: \(\left(\dfrac{1}{16}\right)^x=\left(\dfrac{1}{8}\right)^{36}\)
=>\(\left(\dfrac{1}{2}\right)^{4x}=\left(\dfrac{1}{2}\right)^{108}\)
=>4x=108
=>x=27
18: \(\left(\dfrac{1}{16}\right)^x=\left(\dfrac{1}{2}\right)^3\)
=>\(\left(\dfrac{1}{2}\right)^{4x}=\left(\dfrac{1}{2}\right)^3\)
=>4x=3
=>\(x=\dfrac{3}{4}\)
19: \(\left(\dfrac{1}{32}\right)^x=\left(\dfrac{1}{8}\right)^{15}\)
=>\(\left(\dfrac{1}{2}\right)^{5x}=\left(\dfrac{1}{2}\right)^{45}\)
=>5x=45
=>x=9
20: \(\left(\dfrac{1}{9}\right)^x=\left(\dfrac{1}{27}\right)^6\)
=>\(\left(\dfrac{1}{3}\right)^{2x}=\left(\dfrac{1}{3}\right)^{18}\)
=>2x=18
=>x=9
21: \(\left(\dfrac{1}{9}\right)^x=\left(\dfrac{1}{27}\right)^{22}\)
=>\(\left(\dfrac{1}{3}\right)^{2x}=\left(\dfrac{1}{3}\right)^{66}\)
=>2x=66
=>x=33
22: \(\left(\dfrac{1}{81}\right)^x=\left(\dfrac{1}{27}\right)^4\)
=>\(\left(\dfrac{1}{3}\right)^{4x}=\left(\dfrac{1}{3}\right)^{12}\)
=>4x=12
=>x=3
23: \(\left(\dfrac{4}{9}\right)^x=\left(\dfrac{8}{27}\right)^6\)
=>\(\left(\dfrac{2}{3}\right)^{2x}=\left(\dfrac{2}{3}\right)^{18}\)
=>2x=18
=>x=9
24: \(\left(\dfrac{4}{9}\right)^x=\left(\dfrac{8}{27}\right)^{10}\)
=>\(\left(\dfrac{2}{3}\right)^{2x}=\left(\dfrac{2}{3}\right)^{30}\)
=>\(2x=30\)
=>x=15
