Câu 8:
\(2\cdot3^x+5\cdot3^{x+1}=153\)
=>\(2\cdot3^x+5\cdot3^x\cdot3=153\)
=>\(17\cdot3^x=153\)
=>\(3^x=\dfrac{153}{17}=9=3^2\)
=>x=2
Câu 9:
\(2^{x-1}+2^x+2^{x+1}=112\)
=>\(2^x\cdot\dfrac{1}{2}+2^x+2^x\cdot2=112\)
=>\(2^x\left(2+1+\dfrac{1}{2}\right)=112\)
=>\(2^x\cdot3,5=112\)
=>\(2^x=32=2^5\)
=>x=5
Câu 7:
\(14\cdot7^{2021}=35\cdot7^{2021}-3\cdot49^x\)
=>\(14\cdot7^{2021}-35\cdot7^{2021}=-3\cdot49^x\)
=>\(-21\cdot7^{2021}=-3\cdot49^x\)
=>\(-3\cdot7^{2022}=-3\cdot49^x\)
=>\(49^x=7^{2022}\)
=>\(7^{2x}=7^{2022}\)
=>2x=2022
=>x=1011
Câu 10:
\(2^x+2^{x+1}+2^{x+2}+2^{x+3}=480\)
=>\(2^x+2^x\cdot2+2^x\cdot4+2^x\cdot8=480\)
=>\(2^x\left(1+2+4+8\right)=480\)
=>\(2^x\cdot15=480\)
=>\(2^x=32\)
=>x=5
Câu 11:
\(7^x+7^{x+2}+7^{x+3}=2751\)
=>\(7^x\cdot1+7^x\cdot49+7^x\cdot343=2751\)
=>\(7^x\cdot393=2751\)
=>\(7^x=7\)
=>x=1
Câu 13:
\(5^x\cdot5^{x+1}\cdot5^{x+2}=10000...000:2^{18}\)(18 chữ số 0)
=>\(5^{x+x+1+x+2}=10^{18}:2^{18}=5^{18}\)
=>3x+3=18
=>3x=15
=>x=5
