Question

Giải các Phương trình sau:

a, \(3^{2x+1}-4\cdot3^x+1=0\)  (2)

b, \(log_3\left(9x\right)+log_9x=5\)  (3)

 

Answer 1

a.

\(\Leftrightarrow3.3^{2x}-4.3^x+1=0\)

\(\Leftrightarrow\left(3^x-1\right)\left(3.3^x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}3^x=1\\3^x=\dfrac{1}{3}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)

b.

ĐKXĐ: \(x>0\)

\(log_39+log_3x+\dfrac{1}{2}log_3x=5\)

\(\Leftrightarrow\dfrac{3}{2}log_3x=3\)

\(\Leftrightarrow log_3x=2\Rightarrow x=9\)