Question

Tìm x, biết:

a. \(\left(2x-3^2\right)=25\)

b. \(\dfrac{27}{3^x}=3\)

c. \(9^{x-1}=\dfrac{1}{9}\)

d. \(3^{x+1}+3^{x+3}=810\)

Answer 1

a. \(\left(2x-3^2\right)=25\Rightarrow2x=25+3^2=25+9=34\)

\(\Rightarrow x=34:2=17\)

Vậy x = 17

b. \(\dfrac{27}{3^x}=3\Rightarrow3^x=27:3=9\Rightarrow3^x=3^2\Rightarrow x=2\)

Vậy x = 2

c. \(9^{x-1}=\dfrac{1}{9}\Rightarrow3^{2x-2}=3^{-2}\)

\(2x-2=-2\Rightarrow2x=-2+2=0\Rightarrow x=0\)

Vậy x = 0

d. \(3^{x+1}+3^{x+3}=810\Rightarrow\left(1+3^2\right)\cdot3^{x+1}=810\)

\(\Rightarrow\left(1+9\right)\cdot3^{x+1}=810\Rightarrow10\cdot3^{x+1}=810\)

\(\Rightarrow3^{x+1}=81\Rightarrow3^{x+1}=3^4\Rightarrow x+1=4\Rightarrow x=3\)

Vậy x = 3