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a) (2x)5 : 43 = 815 => 25x = 815.43 = (23)15.(22)3 = 245.26 = 251 => 5x = 51 => x = 10,2
b) (32)x .93 = 2439 => 32x = 2439 : 93 = (35)9 : (32)3 = 345 : 36 = 339 => 2x = 39 => x = 19,5
c) (1/125)3.5x = 255 => 5x = 255 : (1/125)3 = (52)5 : (1/53)3 = 510 : (5-3)3 = 510 : 5-9 = 519 => x = 19
d) 1/81 : 3x = 1/729 => 3x = 1/81 : 1/729 = 1/34.729 = 3-4.36 = 32 => x = 2
e) (5x - 2)4 = 168 = (162)4 = 2564
=> 5x - 2 = -256 ; 256 => 5x = -254 ; 258 => x = -50,8 ; 51,6
P/S : Thay x = 10,2 vào câu a , x = 19,5 vào câu b sẽ thấy điều hư cấu : 210,2 và 919,5.Ko thể tính được giá trị của 2 lũy thừa này.
\(\Rightarrow\left(\frac{\frac{31}{36}}{\frac{11}{9}:4-\frac{3}{4}}:31\right).x=\frac{-1}{16}\Rightarrow\left(\frac{\frac{31}{36}}{\frac{-4}{9}}:31\right)x=-\frac{1}{16}\Rightarrow\left(-\frac{31}{16}:31\right)x=-\frac{1}{16}\Rightarrow-\frac{1}{16}x=-\frac{1}{16}\Rightarrow x=1\)
\(1.\left(-\dfrac{1}{2}\cdot x+0,9\right)^4=\dfrac{16}{81}\)
\(\Rightarrow\left(-\dfrac{1}{2}\cdot x+0,9\right)^4=\left(\pm\dfrac{2}{3}\right)^4\)
\(\Rightarrow\left[{}\begin{matrix}-\dfrac{1}{2}\cdot x+0,9=\dfrac{2}{3}\\-\dfrac{1}{2}\cdot x+0,9=-\dfrac{2}{3}\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}-\dfrac{1}{2}\cdot x=\dfrac{2}{3}-0,9\\-\dfrac{1}{2}\cdot x=-\dfrac{2}{3}-0,9\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}-\dfrac{1}{2}\cdot x=-\dfrac{7}{30}\\-\dfrac{1}{2}\cdot x=-\dfrac{47}{30}\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{7}{30}:-\dfrac{1}{2}\\x=-\dfrac{47}{30}:-\dfrac{1}{2}\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{15}\\x=\dfrac{47}{15}\end{matrix}\right.\)
Vậy \(x\in\left\{\dfrac{7}{15};\dfrac{47}{15}\right\}\)
\(2.\left(\dfrac{4}{3}\right)^{n-2}=\dfrac{16}{9}\)
\(\Rightarrow\left(\dfrac{4}{3}\right)^{n-2}=\left(\dfrac{4}{3}\right)^2\)
\(\Rightarrow n-2=2\)
\(\Rightarrow n=2+2\)
\(\Rightarrow n=4\)
Vậy \(n=4\)
\(3.\left(\dfrac{1}{2}\right)^{2n-1}=\dfrac{1}{8}\)
\(\Rightarrow\left(\dfrac{1}{2}\right)^{2n-1}=\left(\dfrac{1}{2}\right)^3\)
\(\Rightarrow2n-1=3\)
\(\Rightarrow2n=3+1\)
\(\Rightarrow2n=4\)
\(\Rightarrow n=4:2\)
\(\Rightarrow n=2\)
Vậy \(n=2\)
\(4.\left(-\dfrac{4}{5}\right)^{3n+1}=\dfrac{16}{25}\)
\(\Rightarrow\left(-\dfrac{4}{5}\right)^{3n+1}=\left(-\dfrac{4}{5}\right)^2\)
\(\Rightarrow3n+1=2\)
\(\Rightarrow3n=2-1\)
\(\Rightarrow3n=1\)
\(\Rightarrow n=1:3\)
\(\Rightarrow n=\dfrac{1}{3}\)
Vậy \(n=\dfrac{1}{3}\)