Question

Logarit

3.8^x+4.12^x-18^x-2.27^x=0

Answer 1

Chia 2 vế cho \(27^x\) ta được:

\(3\left(\dfrac{8}{27}\right)^x+4\left(\dfrac{12}{27}\right)^x-\left(\dfrac{18}{27}\right)^x-2=0\)

\(\Leftrightarrow3\left(\dfrac{2}{3}\right)^{3x}+4\left(\dfrac{2}{3}\right)^{2x}-\left(\dfrac{2}{3}\right)^x-2=0\)

Đặt \(\left(\dfrac{2}{3}\right)^x=t>0\)

\(\Rightarrow3t^3+4t^2-t-2=0\)

\(\Leftrightarrow\left(t+1\right)^2\left(3t-2\right)=0\)

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

\(\Rightarrow x=1\)