\(4,2^{x+2}-2^x=96\\ =>2^x\cdot\left(2^2-1\right)=96\\ =>2^x\cdot3=96\\ =>2^x=96:3=32\\ =>2^x=2^5\\ =>x=5\\ 5,2^{x+3}+2^x=144\\ =>2^x\cdot\left(2^3+1\right)=144\\ =>2^x\cdot9=144\\ =>2^x=\dfrac{144}{9}=16\\ =>2^x=2^4\\ =>x=4\\ 6,3^{x+3}-3^x=234\\ =>3^x\cdot\left(3^3-1\right)=234\\ =>3^x\cdot26=234\\ =>3^x=9\\ =>3^x=3^2\\ =>x=2\)
`4, 2^(x+2) - 2^x = 96`
`=> 2^x . 2^2 - 2^x = 96`
`=> 2^x . 4 - 2^x . 1 = 96`
`=> 2^x . (4 - 1) =96`
`=> 2^x .3 = 96`
`=> 2^x = 32`
`=> 2^x = 2^5`
`=> x=5`
Vậy: `x=5`
`5, 2^(x+3)+2^x=144`
`=> 2^x . 2^3+ 2^x . 1 = 144`
`=> 2^x . (8+1)=144`
`=> 2^x . 9 = 144`
`=> 2^x = 16`
`=>2^x=2^4`
`=> x=4`
Vậy: `x=4`
`6, 3^(x+3)-3^x=234`
`=> 3^x . 3^3- 3^x . 1 = 234`
`=> 3^x . (27-1)=234`
`=> 3^x= 234:26`
`=> 3^x=9`
`=> 3^x = 3^2`
`=> x=2`
Vậy: `x=2`
\(7,5^x+5^{x+1}=750\\ =>5^x\cdot\left(1+5\right)=750\\ =>5^x\cdot6=750\\ =>5^x=\dfrac{750}{6}=125\\ =>5^x=5^3\\ =>x=3\\ 8,2^x+2^{x+2}=320\\ =>2^x\cdot\left(1+2^2\right)=320\\ =>2^x\cdot5=320\\ =>2^x=\dfrac{320}{5}=64\\ =>2^x=2^6\\ =>x=6\\ 9,5^x+5^{x+2}=650\\ =>5^x\cdot\left(1+5^2\right)=650\\ =>5^x\cdot26=650\\ =>5^x=\dfrac{650}{26}\\ =>5^x=25\\ =>5^x=5^2\\ =>x=2\)
