b: =>(2/3)^5x-1=(2/3)^16
=>5x-1=16
=>5x=17
=>x=17/5
c: =>3^3x*3^2=3^x
=>3x-2=x
=>2x=2
=>x=1
d: =>5*2^x-2^x*2=192
=>3*2^x=192
=>2^x=64
=>x=6
\(b,\left(\dfrac{2}{3}\right)^{5x-1}=\left(-\dfrac{4}{9}\right)^8\\ \Leftrightarrow\left(\dfrac{2}{3}\right)^{5x-1}=\left(\dfrac{4}{9}\right)^8=\left(\dfrac{2}{3}\right)^{2.8}=\left(\dfrac{2}{3}\right)^{16}\\ nên:5x-1=16\\ \Leftrightarrow5x=17\\ \Leftrightarrow x=\dfrac{17}{5}\\ c,\dfrac{1}{9}.27^x=3^x\\ \Leftrightarrow\dfrac{1}{3^2}.\left(3^3\right)^x=3^x\\ \Leftrightarrow\dfrac{3^{3x}}{3^2}=3^x\\ \Leftrightarrow3^{3x-2}=3^x\\ Nên:3x-2=3\\ \Leftrightarrow3x=5\\ \Leftrightarrow x=\dfrac{5}{3}\)
d,
\(5.2^x-2^{x+1}-192=0\\ \Leftrightarrow2^x.\left(5-2\right)=192\\ \Leftrightarrow3.2^x=192\\ \Leftrightarrow2^x=\dfrac{192}{3}=64\\ Mà:64=2^6\\ Vậy:x=6\)
