Question

tìm x:

a) 3^x+2 - 8 . 3^x = 81

b) (x-1)² = (x-1)³

Answer 1

a, 3^x+2 - 8.3^x = 81
<=> 3^x.9 - 8.3^x = 81
<=> 3^x(9 - 8) = 81
<=> 3^x = 81
<=> 3^x = 3⁴
<=> x = 4
b, (x - 1)² = (x - 1)³
<=> (x - 1)² - (x - 1)³ = 0
<=> (x - 1)².[1 - (x - 1)] = 0
<=> (x - 1)².(1 - x + 1) = 0
<=> (x - 1)².(2 - x) = 0
<=> \(\left[{}\begin{matrix}\left(x-1\right)^2=0\\2-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x=2\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\) (thỏa mãn)
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