a. 16x < 1284
<=> 16x < 167
<=> x < 7
Vậy nghiệm của BPT là \(S=\left\{x|x< 7\right\}\)
\(a,16^x< 128^4\Leftrightarrow2^{4x}< 2^{28}\\ \Leftrightarrow4x=28\Leftrightarrow x=7\\ b,5^x\cdot5^{x+1}\cdot5^{x+2}< 1000...0:2^{18}\\ \Leftrightarrow5^{3x+3}< 10^{18}:2^{18}\\ \Leftrightarrow5^{3x+3}< 5^{18}\cdot2^{18}:2^{18}=5^{18}\\ \Leftrightarrow3x+3=18\\ \Leftrightarrow x=5\)
\(c,\) Ta có \(100>5^2;100< 5^3\)
\(\Rightarrow5^2\cdot2^2< 5^{2x-1}\le5^6\Rightarrow5^2< 5^{2x-1}\le5^6\\ \Rightarrow2< 2x-1\le6\\ \Rightarrow2x-1\in\left\{3;4;5;6\right\}\\ \Rightarrow x\in\left\{2;3\right\}\left(x\in N\right)\)
