1) \(7.4^x=7.4^3\Leftrightarrow4^x=4^3;x=3\)

2) \(\frac{3}{2.5^x}=\frac{3}{2.5^{12}}\Leftrightarrow5^x=5^{12};x=12\)

\(2^x=2.2^8=2^9;x=9\)

4) \(5.3^x=7.3^5-2.3^5\Leftrightarrow5.3^x=3^5.\left(7-2\right)\)

\(\Leftrightarrow3^5.x=3^5.5;x=5\)

a) (2x-1)³=-8=> 2x-1=-2

<=> 2x=-1=> x=-1/2

b) 

7.3^x=5.3⁷+2.3⁷=(5+2).3⁷=7.3⁷

=> x=7

a, ( 2x - 1 )³ = -8

\(\Rightarrow\)  2x - 1 = -2

      2x       =   -2 + 1

      2x       =  -1

      x         = -1 : 2 = \(\frac{-1}{2}\) 

b, 7 . 3^x =  5 . 3⁷ + 2 . 3⁷

     7.3^x  = ( 5 + 2 ) . 3⁷

     7.3^x  = 7. 3⁷

Vậy x = 7

1. \(\left(-\dfrac{3}{2}\right)^2=\dfrac{9}{4}\)

\(\Rightarrow\left(-\dfrac{3}{2}\right)^x=\left(-\dfrac{3}{2}\right)^2\)

\(\Rightarrow x=2\)

2.\(3^{2x+2}=9^{10}\)

\(\Rightarrow3^{2x+2}=\left(3^2\right)^{10}\)

\(\Rightarrow3^{2x+2}=3^{20}\)

\(\Rightarrow2x+2=20\)

\(\Rightarrow2x=18\)

\(\Rightarrow x=9\)

3)\(3^{3-2x}=27^{13}\)

\(\Rightarrow3^{3-2x}=\left(3^3\right)^{13}\)

\(\Rightarrow3^{3-2x}=3^{39}\)

\(\Rightarrow3-2x=39\)

\(\Rightarrow2x=-36\)

\(\Rightarrow x=-18\)

4)\(5.3^x=7.3^5-2.3^5\)

\(\Rightarrow5.3^x=3^5\left(7-2\right)\)

\(\Rightarrow5.3^x=3^5.5\)

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

\(\Rightarrow x=5\)

\(c=\frac{1}{99.97}-\left(\frac{1}{97.95}+\frac{1}{95.93}+\frac{1}{93.91}+...+\frac{1}{5.3}+\frac{1}{3.1}\right)\)

\(c=\frac{1}{99.97}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{95}-\frac{1}{97}\right)\)

\(c=\frac{1}{99.97}\left(1-\frac{1}{97}\right)\)

\(c=\frac{1}{99.97}.\frac{96}{97}\)

\(c=\frac{32}{33.97.97}\)

bai hoang lan sai roi

\(9^{x+1}+5.3^{2x}=324\)

\(9^x.9+5.\left(3^2\right)^x=324\)

\(9^x.9+5.9^x=324\)

\(9^x.\left(5+9\right)=324\)

\(9^x.14=324\)

\(9^x=\frac{324}{14}\)

\(\Rightarrow x\in\varnothing\)

\(9^{x+1}-5.3^{2x}=324\)

\(\Rightarrow9^x.9-5.9^x=324\)

\(\Rightarrow9^x\left(9-5\right)=324\)

\(\Rightarrow9^x.4=324\)

\(\Rightarrow9^x=81\)

\(\Rightarrow9^x=9^2\)

vậy x=2

\(\Rightarrow x=2\)

\(9^{x+1}-5.3^{2x}=324\)

\(9^x.9-5.9^x=324\)

\(9^x.\left(9-5\right)=324\)

\(9^x.4=324\)

\(9^x=81=9^2\)

\(\Rightarrow x=2\)

a) 5^{x + 1} - 2.5^x = 75

<=> 5^x.5 - 2.5^x = 75

<=> 5^x.3 = 75

<=> 5^x = 25

<=> 5^x = 5²

<=> x = 2

Vậy x = 2

b) 9^{x + 1} -  5.3^2x = 324

<=> (3²)^{x + 1} - 5.3^2x = 324

<=> 3^{2x + 2} - 5.3^2x = 324

<=> 3^2x.3² - 5.3^2x = 324

<=> 3^2x . 4 = 324

<=> 3^2x = 81

<=> 3^2x = 3⁴

<=> 2x = 4

<=> x = 2

Vậy x = 2

UIUYI