1: =>\(5^{x-2}-9=2^4-\left(6^2-6^2\right)\)

=>\(5^{x-2}=16+9=25\)

=>x-2=2

=>x=4

2: \(\Leftrightarrow3^x+16=19^6:19^5-3=19-3=16\)

=>3^x=0

=>x=0

3: \(\Leftrightarrow2^x+2^x\cdot16=272\)

=>2^x*17=272

=>2^x=16

=>x=4

4: \(\Leftrightarrow2^{x-1}+3=24-\left(4^2-2^2+1\right)=24-\left(16-4+1\right)\)

=>\(2^{x-1}+3=24-16+4-1=8+4-1=12-1=11\)

=>2^x-1=8

=>x-1=3

=>x=4

`1/3 : (2x - 1) = (-4/24)`

`2x - 1 = 1/3 : (-4/24)`

`2x - 1 = -2`

`2x = (-2) + 1`

`2x = (-1)`

`x = 2 : (-1)`

`x = -2`

\(\dfrac{1}{3}:\left(2x-1\right)=\dfrac{-4}{24}\)

        \(2x-1=\dfrac{1}{3}:\left(\dfrac{-4}{24}\right)\)

        \(2x-1=-2\)

        \(2x=\left(-2\right)+1\)

         \(2x=-1\)

           \(x=2:\left(-1\right)\)

           \(x=-2\)

vậy x =...

\(5x\left(x-2\right)-3\left(x-1\right)=20x^2-15x\left(2x+1\right)-24\)

\(\Rightarrow5x^2-10x-3x+3=20x^2-30x^2-15x-24\)

\(\Rightarrow5x^2-13x+3=-10x^2-15x-24\)

\(\Rightarrow5x^2+10x^2-13x+15x+3+24=0\)

\(\Rightarrow15x^2+2x+27=0\)

Ta có: 

\(\Delta=2^2-4\cdot15\cdot27==-1616< 0\)

Nên pt vô nghiệm

\(5x\left(x-2\right)-3\left(x-1\right)=20x^2-15x\left(2x+1\right)-24\\ \Leftrightarrow5x^2-10x-3x+3=20x^2-30x^2-15x-24\\ \Leftrightarrow5x^2-20x^2+30x^2-10x-3x+15x+3+24=0\\ \Leftrightarrow15x^2+2x+27=0\\ \Leftrightarrow15x^2-2.x.\sqrt{15}+\dfrac{2}{15}+\dfrac{403}{15}=0\\ \Leftrightarrow\left(\sqrt{15}x+\dfrac{\sqrt{30}}{15}\right)^2+\dfrac{403}{15}=0\left(Vô.lí\right)\\ Vậy:Không.có.x.thoả\)

a: \(x^3=27\)

=>\(x^3=3^3\)

=>x=3

b: \(\left(2x-1\right)^3=8\)

=>\(\left(2x-1\right)^3=2^3\)

=>2x-1=2

=>2x=2+1=3

=>\(x=\frac32=1,5\)

c: \(\left(x-2\right)^2=16\)

=>\(\left[\begin{array}{l}x-2=4\\ x-2=-4\end{array}\right.\Rightarrow\left[\begin{array}{l}x=4+2=6\\ x=-4+2=-2\end{array}\right.\)

d: \(\left(2x-3\right)^2=9\)

=>\(\left[\begin{array}{l}2x-3=3\\ 2x-3=-3\end{array}\right.\Longrightarrow\left[\begin{array}{l}2x=6\\ 2x=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=3\\ x=0\end{array}\right.\)

e: \(2x+5=3^4:3^2\)

=>\(2x+5=3^2=9\)

=>2x=9-5=4

=>\(x=\frac42=2\)

f: \(\left(3x-2^4\right)\cdot7^3=2\cdot7^4\)

=>\(3x-16=2\cdot\frac{7^4}{7^3}=2\cdot7=14\)

=>3x=16+14=30

=>\(x=\frac{30}{3}=10\)

a: \(x^3=27\)

=>\(x^3=3^3\)

=>x=3

b: \(\left(2x-1\right)^3=8\)

=>\(\left(2x-1\right)^3=2^3\)

=>2x-1=2

=>2x=2+1=3

=>\(x=\frac32=1,5\)

c: \(\left(x-2\right)^2=16\)

=>\(\left[\begin{array}{l}x-2=4\\ x-2=-4\end{array}\right.\Rightarrow\left[\begin{array}{l}x=4+2=6\\ x=-4+2=-2\end{array}\right.\)

d: \(\left(2x-3\right)^2=9\)

=>\(\left[\begin{array}{l}2x-3=3\\ 2x-3=-3\end{array}\right.\Longrightarrow\left[\begin{array}{l}2x=6\\ 2x=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=3\\ x=0\end{array}\right.\)

e: \(2x+5=3^4:3^2\)

=>\(2x+5=3^2=9\)

=>2x=9-5=4

=>\(x=\frac42=2\)

f: \(\left(3x-2^4\right)\cdot7^3=2\cdot7^4\)

=>\(3x-16=2\cdot\frac{7^4}{7^3}=2\cdot7=14\)

=>3x=16+14=30

=>\(x=\frac{30}{3}=10\)

x^2 -2x = 24

=> x^2 - 2x - 24=0

=>x^2 -8x+6x - 24 = 0

=> ( x^2- 8x)+( 6x-24) = 0

=> x(x-8) + 6(x-8) = 0

=> (x+6)(x-8)=0

=>\(\orbr{\begin{cases}x=-6\\x=8\end{cases}}\)

\(=\frac{\left(2.5\right)^4.3^4-2^4\left(3.5\right)^2}{2^8.5^2.3^3}=\frac{2^4.3^2.5^2\left(5^2.3^2-1\right)}{2^8.5^2.3^3}=\frac{255-1}{16.3}=\frac{14}{3}\)