a)

\(3^x+3^{x+1}+3^{x+2}=117\\ \Leftrightarrow3^x+3.3^x+9.3^x=117\\ 13.3^x=117\\ \Leftrightarrow3^x=9\\ \Leftrightarrow3^x=3^2\\ \Leftrightarrow x=2\)

b)

 \(3+4\left(x-10\right)=3^2+6\\ \Leftrightarrow3+4\left(x-10\right)=15\\ \Leftrightarrow4\left(x-10\right)=12\\ \Leftrightarrow x-10=3\\ \Leftrightarrow x=13\)

a) \(3^x+3^{x+1}+3^{x+2}=117\)

\(3^x+3^x.3+3^x.3^2=117\)

\(3^x.\left(1+3+3^2\right)=117\)

\(3^x.13=117\)

\(3^x=9\)

\(x=2\)

b) \(3+4\left(x-10\right)=3^2+6\)

\(3+4x-40=9+6\)

\(4x=15+40-3\)

\(4x=52\)

\(x=13\)

(x+1) + (x+2) + ... + (x+30) = 795

=> 30x + (1+2+... +30) = 795

=> 30x + 465 = 795

=> 30x = 330

=> x = 11

`21-(x-20)=10`

`x-20=21-10`

`x-20=11`

`x=11+20`

`x=31`

x-20=21-10 => x-20=11 =>x=11+20= 31

Mình không xuống dòng, viết gạch nối nhé

\(3^{x+1}+3^{x+3}+3^{x+5}=813\)

\(3^x.3+3^x.3^3+3^x.3^5=813\)

\(3^x.\left(3+3^3+3^5\right)=813\)

\(3^x.\left(3+27+243\right)=813\)

\(3^x.273=813\) -> kiểm tra lại đề

Mình xin lỗi mình không giỏi kĩ thuât lắm nên dòng viết hơi sộc sệch 

Mình cũng lớp 6 nè, nhưng mình bận quá không có thời gian để nghĩ,sorry bạn nhìu nhoa=)))

\(a,4^3.8^2.27^4=\left(2^2\right)^3.\left(2^3\right)^2.\left(3^3\right)^4=2^6.2^6.3^{12}=2^{12}.3^{12}=\left(2.3\right)^{12}=6^{12}\\ b,27^4.81^2.16^5=\left(3^3\right)^4.\left(3^4\right)^2.\left(2^4\right)^5=3^{12}.3^8.2^{20}=3^{20}.2^{20}=\left(3.2\right)^{20}=6^{20}\\ c,5^3.25^4.125^2=5^3.\left(5^2\right)^4.\left(5^3\right)^2=5^3.5^8.5^6=5^{3+8+6}=5^{17}\\ d,10^2.100^3.1000000^3=10^2.\left(10^2\right)^3.\left(10^6\right)^3=10^2.10^6.10^{18}=10^{2+6+18}=10^{26}\)