a) \(5\left(x+7\right)-10=2^3\cdot5\)

\(\Rightarrow5\left(x+7\right)-10=40\)

\(\Rightarrow5\left(x+7\right)=40+10\)

\(\Rightarrow x+7=\dfrac{50}{5}\)

\(\Rightarrow x+7=10\)

\(\Rightarrow x=10-7\)

\(\Rightarrow x=3\)

b) \(9x-2\cdot3^2=3^4\)

\(\Rightarrow9x-18=81\)

\(\Rightarrow9x=81+18\)

\(\Rightarrow9x=99\)

\(\Rightarrow x=\dfrac{99}{9}\)

\(\Rightarrow x=11\)

c) \(5^{25}\cdot5^{x-1}=5^{25}\)

\(\Rightarrow5^{x-1}=5^{25}:5^{25}\)

\(\Rightarrow5^{x-1}=1\)

\(\Rightarrow5^{x-1}=5^0\)

\(\Rightarrow x-1=0\)

\(\Rightarrow x=1\)

a) $5\left(x+7\right)-10=2^3\cdot 5$

$\Rightarrow 5\left(x+7\right)-10=40$

$\Rightarrow 5\left(x+7\right)=40+10$

$\Rightarrow x+7=\genfrac{}{}{0ex}{}{50}{5}$

$\Rightarrow x+7=10$

$\Rightarrow x=10-7$

$\Rightarrow x=3$

b) $9x-2\cdot 3^2=3^4$

$\Rightarrow 9x-18=81$

$\Rightarrow 9x=81+18$

$\Rightarrow 9x=99$

$\Rightarrow x=\genfrac{}{}{0ex}{}{99}{9}$

$\Rightarrow x=11$

c) $5^{25}\cdot 5^{x-1}=5^{25}$

$\Rightarrow 5^{x-1}=5^{25}:5^{25}$

$\Rightarrow 5^{x-1}=1$

$\Rightarrow 5^{x-1}=5^0$

$\Rightarrow x-1=0$

$\Rightarrow x=1$

\(A=3^5=243;B=2^8=256\Rightarrow A< B\)

A=35=243;B=28=256⇒A<B

vãi nồn

                A   =      5 - 5² + 5³ - 5⁴ +...+ 5⁹⁷ - 5⁹⁸ + 5⁹⁹

              5A   =           5²  - 5³ + 5⁴-.....-5⁹⁷ + 5⁹⁸ - 5⁹⁹ + 5¹⁰⁰

         5A +  A =  5 + 5¹⁰⁰

                6A   = 5 + 5¹⁰⁰

                 A = \(\dfrac{5+5^{100}}{6}\)

\(\left(2^3\cdot x-4^2\right)\left(x-2^2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}2^3\cdot x-4^2=0\\x-2^2=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}8\cdot x=16\\x=2^2\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{16}{8}=2\\x=4\end{matrix}\right.\)

$\left(2^3\cdot x-4^2\right)\left(x-2^2\right)=0$

$\Rightarrow [\begin{array}{c}{2}^3\cdot x-4^2=0\\ x-2^2=0\end{array}$

$\Rightarrow [\begin{array}{c}8\cdot x=16\\ x=2^2\end{array}$

$\Rightarrow [\begin{array}{c}x=\genfrac{}{}{0ex}{}{16}{8}=2\\ x=4\end{array}$
 

1) \(2^x=4^3 \Leftrightarrow2^x=2^6\Leftrightarrow x=6\)

2) \(2^x=4^6\Leftrightarrow2^x=2^{12}\Leftrightarrow x=12\)

3) \(3^x=9^{10}\Leftrightarrow3^x=3^{20}\Leftrightarrow x=20\)

1) $2^x=4^3\iff 2^x=2^6\iff x=6$

2) $2^x=4^6\iff 2^x=2^{12}\iff x=12$

3) $3^x=9^{10}\iff 3^x=3^{20}\iff x=20$