Question

a) 9^x -5*6^x+4^x+1=0

b) 3*25^x+2*49^x-5*35^x=0

Answer 1

a. 3^2x - 5.(3.2)^x + 2^2x.4 =0

(=) \(\left(\dfrac{3}{2}\right)^{^{2x}}-5.\left(\dfrac{3}{2}\right)^x+2^{2x}.4\) =0

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

=> pttt: t² - 5t +4 =0

(=)\(\left[{}\begin{matrix}t=1\\t=4\end{matrix}\right.\)

(=) \(\left[{}\begin{matrix}\left(\dfrac{3}{2}\right)^x=1\\\left(\dfrac{3}{2}\right)^x=4\end{matrix}\right.\)

(=)\(\left[{}\begin{matrix}x=0\\x=\log_{\dfrac{3}{2}}4\end{matrix}\right.\)

Answer 2

b. 3.5^2x + 2.7^2x - 5.(5.7)^x =0

(=) \(3+2.\left(\dfrac{7}{5}\right)^{2x}-5.\left(\dfrac{7}{5}\right)^x=0\)

đặt \(t=\left(\dfrac{7}{5}\right)^x\) đk: t > 0

pttt: 3+2t²-5t=0

(=) \(\left[{}\begin{matrix}t=1\\t=\dfrac{3}{2}\end{matrix}\right.\)

(=)\(\left[{}\begin{matrix}x=0\\x=\log_{\dfrac{7}{5}}\dfrac{3}{2}\end{matrix}\right.\)