Question

Tìm x , y :

a , \(\frac{2}{3}.3^{x+1}-7.3^x=-405\)

b , \(\left(0,4x-1,3\right)^2=5,29\)

c , \(5.2^{x+1}.2^{-2}-2^x=384\)

d , \(3^{x+2}.5^y=45^x\)

e , \(4^x+4^{x+3}=4160\)

f , \(2^{x-1}+5.2^{x-2}=\frac{7}{32}\)

Answer 1

a/ \(\frac{2}{3}.3^{x+1}-7.3^x=405\)

<=> 2.3^x-7.3^x=-405

<=> 5.3^x=405

<=> 3^x=81 = 3⁴

=> x=4

b/ (0,4x-1,3)²=5,29=(2,3)²

=> \(\hept{\begin{cases}0,4x-1,3=2,3\\0,4x-1,3=-2,3\end{cases}}\)=> \(\hept{\begin{cases}x=9\\x=-\frac{5}{2}\end{cases}}\)

c/ 5.2^x+1.2^-2-2^x=384

<=> 5.2^x-1-2.2^x-1=384

<=> 3.2^x-1=384

<=> 2^x-1=128=2⁷

=> x-1=7 => x=8

d/ 3^x+2.5^y=45^x

<=> 3^x+2.5^y=3^2x.5^x

=> \(\hept{\begin{cases}x+2=2x\\x=y\end{cases}}\)=> x=y=2