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(�+7)−10=23⋅55(x+7)−10=23⋅5

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

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

⇒�+7=505⇒x+7=550​

$\Rightarrow x+7=10$

$\Rightarrow x=10-7$

$\Rightarrow x=3$

b) 9�−2⋅32=349x−2⋅32=34

$\Rightarrow 9x-18=81$

$\Rightarrow 9x=81+18$

$\Rightarrow 9x=99$

⇒�=999⇒x=999​

$\Rightarrow x=11$

c) 525⋅5�−1=525525⋅5x−1=525

⇒5�−1=525:525⇒5x−1=525:525

⇒5�−1=1⇒5x−1=1

⇒5�−1=50⇒5x−1=50

$\Rightarrow x-1=0$

$\Rightarrow x=1$

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

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 = \(\dfrac{5+5^{100}}{6}\)

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

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

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

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

(23⋅x−42)(x−22)=0

⇒[23⋅�−42=0�−22=0⇒[23⋅x−42=0x−22=0​

⇒[8⋅�=16�=22⇒[8⋅x=16x=22​

⇒[�=168=2�=4⇒[x=816​=2x=4​
 

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�=43⇔2�=26⇔�=62x=43⇔2x=26⇔x=6

2) 2�=46⇔2�=212⇔�=122x=46⇔2x=212⇔x=12

3) 3�=910⇔3�=320⇔�=203x=910⇔3x=320⇔x=20