Tìm x biết :
e ) x: ( $\frac{-1}{3}$ )$^{3}$ = $\frac{-1}{3}$
f ) ( $\frac{-3}{5}$ )$^{2}$ × x = ( $\frac{3}{5}$ )$^{2}$
g) $\frac{x×x}{27}$ = 81
h) $\frac{xmũ8}{9}$ = 729
Tìm x biết :
e ) x: ( $\frac{-1}{3}$ )$^{3}$ = $\frac{-1}{3}$
f ) ( $\frac{-3}{5}$ )$^{2}$ × x = ( $\frac{3}{5}$ )$^{2}$
g) $\frac{x×x}{27}$ = 81
h) $\frac{xmũ8}{9}$ = 729
Đáp án:
$\\$
`e,`
`x ÷ (-1/3)^3 = (-1)/3`
`↔ x = (-1)/3 × (-1/3)^3`
`↔ x = (-1/3)^4`
`↔ x = 1/81`
Vậy `x = 1/81`
$\\$
`f,`
`(-3/5)^2 × x = (3/5)^2`
`↔ x = (3/5)^2 ÷ (-3/5)^2`
`↔ x = (3/5 ÷ (-3)/5)^2`
`↔ x = (-1)^2`
`↔ x= 1`
Vậy `x=1`
$\\$
`g,`
`(x×x)/27 = 81`
`↔ x^2 = 27 × 81`
`↔ x^2 = 2187`
`↔` \(\left[ \begin{array}{l}x^2=(3^{\dfrac{7}{2} })^2\\x^2=(-3^{\dfrac{7}{2} })^2\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=3^{\dfrac{7}{2} }\\x=-3^{\dfrac{7}{2} }\end{array} \right.\)
Vậy $x = 3^{\dfrac{7}{2} }$ hoặc $x = -3^{\dfrac{7}{2} }$
$\\$
`h,`
`x^8/9 = 729`
`↔ x^8 = 9 × 729`
`↔ x^8 = 6561`
`↔` \(\left[ \begin{array}{l}x^8=3^8\\x^8=(-3)^8\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=3\\x=-3\end{array} \right.\)
Vậy `x=3` hoặc `x=-3`
$\begin{array}{l} x:{\left( {\dfrac{{ – 1}}{3}} \right)^3} = \dfrac{1}{3}\\ \Leftrightarrow x = \dfrac{1}{3}.{\left( { – \dfrac{1}{3}} \right)^3} = – \dfrac{1}{3}.{\left( {\dfrac{1}{3}} \right)^3} = – {\left( {\dfrac{1}{3}} \right)^4} \end{array}$
f) $\begin{array}{l} {\left( { – \dfrac{3}{5}} \right)^2}x = {\left( {\dfrac{3}{5}} \right)^2}\\ \Leftrightarrow {\left( {\dfrac{3}{5}} \right)^2}.x = {\left( {\dfrac{3}{5}} \right)^2}\\ \Leftrightarrow x = 1 \end{array}$
$\begin{array}{l} g)\dfrac{{x.x}}{{27}} = 81\\ \Leftrightarrow {x^2} = 81.27 = {3^4}{.3^3} = {3^7}\\ \Rightarrow x = \pm {3^{\dfrac{7}{2}}}\\ h)\dfrac{{{x^8}}}{9} = 729\\ \Leftrightarrow {x^8} = {3^6}.9 = {3^6}{.3^2} = {3^8}\\ \Leftrightarrow \left[ \begin{array}{l} x = 3\\ x = – 3 \end{array} \right. \end{array}$