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 13:
\(5^x\cdot5^{x+1}\cdot5^{x+2}=10000...000:2^{18}\)(18 chữ số 0)
=>\(5^{x+x+1+x+2}=10^{18}:2^{18}=5^{18}\)
=>\(5^{3x+3}=5^{18}\)
=>3x+3=18
=>3x=15
=>x=15/3=5
Câu 14:
\(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+30\right)=1240\)
=>\(31x+\left(1+2+...+30\right)=1240\)
=>\(31x+\dfrac{30\left(30+1\right)}{2}=1240\)
=>\(31x+15\cdot31=1240\)
=>\(31x=1240-15\cdot31=775\)
=>x=25
Câu 11:
\(7^x+7^{x+2}+7^{x+3}=2751\)
=>\(7^x+7^x\cdot49+7^x\cdot343=2751\)
=>\(7^x\left(1+49+343\right)=2751\)
=>\(7^x=7\)
=>x=1
