a) \(3^{2x-1}=243\)

\(\Leftrightarrow3^{2x-1}=3^5\)

\(\Leftrightarrow2x-1=5\)

\(\Leftrightarrow2x=5+1\)

\(\Leftrightarrow2x=6\)

\(\Leftrightarrow x=\dfrac{6}{2}\)

\(\Leftrightarrow x=3\)

Vậy \(x=3\)

b) \(\left(3^x\right)^2:3^3=\dfrac{1}{243}\)

\(\Leftrightarrow3^{2x}:3^3=\dfrac{1}{3^5}\)

\(\Leftrightarrow3^{2x}:3^3=3^{-5}\)

\(\Leftrightarrow3^{2x-3}=3^{-5}\)

\(\Leftrightarrow2x-3=-5\)

\(\Leftrightarrow2x=-5+3\)

\(\Leftrightarrow2x=-2\)

\(\Leftrightarrow x=-\dfrac{2}{2}\)

\(\Leftrightarrow x=1\)

Vậy \(x=1\)

c) \(2^{3x+2}=4^{x+5}\)

\(\Leftrightarrow2^{3x+2}=\left(2^2\right)^{x+5}\)

\(\Leftrightarrow2^{3x+2}=2^{2\left(x+5\right)}\)

\(\Leftrightarrow3x+2=2\left(x+5\right)\)

\(\Leftrightarrow3x+2=2x+10\)

\(\Leftrightarrow3x-2x=10-2\)

\(\Leftrightarrow x=8\)

Vậy \(x=8\)

d) \(3^{x+1}=9^x\)

\(\Leftrightarrow3^{x+1}=\left(3^2\right)^x\)

\(\Leftrightarrow3^{x+1}=3^{2x}\)

\(\Leftrightarrow x+1=2x\)

\(\Leftrightarrow2x-x=1\)

\(\Leftrightarrow x=1\)

Vậy \(x=1\)

`#3107.101107`

a)

\(27< 3^x< 243\\ \Rightarrow3^3< 3^x< 3^5\\ \Rightarrow3< x< 5\\ \Rightarrow x=4\)

Vậy, `x = 4`

b)

\(2^x+2^{x+1}+2^{x+2}=56?\\ \Rightarrow2^x+2^x\cdot2+2^x\cdot4=56\\ \Rightarrow2^x\cdot\left(1+2+4\right)=56\\ \Rightarrow2^x\cdot7=56\\ \Rightarrow2^x=8\\ \Rightarrow2^x=2^3\\ \Rightarrow x=3\)

Vậy, `x = 3`

c)

\(3^x+3^{x+2}=810\\ \Rightarrow3^x+3^x\cdot9=810\\ \Rightarrow3^x\cdot\left(1+9\right)=810\\ \Rightarrow3^x\cdot10=810\\ \Rightarrow3^x=81\\ \Rightarrow3^x=3^4\\ \Rightarrow x=4\)

Vậy, `x = 4.`

a) \(27< 3^x< 243\)

\(\Rightarrow3^3< 3^x< 3^5\)

\(\Rightarrow3< x< 5\)

c) \(3^x+3^{x+2}=810\)

\(\Rightarrow3^x\left(1+3^2\right)=810\)

\(\Rightarrow3^x.10=810\)

\(\Rightarrow3^x=810:10\)

\(\Rightarrow3^x=81\)

\(\Rightarrow3^x=3^4\)

\(\Rightarrow x=4\)

sai đề rồi

\(\Leftrightarrow3^x\cdot3=243\)

hay x=4

\(8;a,3^2.\frac{1}{243}.81^2.\frac{1}{3^3}\)

\(=\frac{3^2.\left(3^4\right)^2}{243.3^3}\)

\(=\frac{3^2.3^8}{3^5.3^3}\)

\(=\frac{3^{10}}{3^8}=3^2=9\)

\(b,\frac{4.2^5}{2^3.\frac{1}{16}}\)

\(=\frac{2^2.2^5}{2^3.\frac{1}{2^4}}\)

\(=\frac{2^7}{\frac{1}{2}}=2^7.2=2^8\)

a, \(3^2.\frac{1}{243}.81^2.\frac{1}{3}^3\)

\(=3^2.\frac{1}{243}.\left(3^4\right)^2.\frac{1}{27}\)

\(=3^2.\frac{1}{243}.3^8.\frac{1}{27}\)

\(=\frac{3^2.3^8}{243.27}\)

\(=\frac{3^2.3^8}{3^5.3^3}\)

\(=\frac{3^{10}}{3^8}=3^2=9\)

b, \(\left(4.2^5\right):\left(2^3.\frac{1}{16}\right)\)

\(=\left(2^2.2^5\right):\left(8.\frac{1}{16}\right)\)

\(=2^7:\frac{1}{2}\)

\(=2^8\)

(3^x)^2=1/243.3^3

(3^x)^2=1/9

3x=1/3 hoặc 3x=-1/3

Suy ra x=1/9 hoặc x=-1/9

3^x( 1 + 3 + 3²) = 3⁶.13

3^x. 13 = 3⁶.13

=> 3^x= 3⁶

=> x= 6

mk ko hiểu cho lắm

bn ko hiểu chỗ nào???