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NT
29 tháng 8 2023 lúc 9:42

b: (1/2)^x=1/32

=>(1/2)^x=(1/2)^5

=>x=5

b: (7/5)^x=343/125

=>(7/5)^x=(7/5)^3

=>x=3

b: (-3/2)^x=9/4

=>(-3/2)^x=(-3/2)^2

=>x=2

b: (-2/3)^x=-8/27

=>(-2/3)^x=(-2/3)^3

=>x=3

b: (3/5)^x+98/125=1

=>(3/5)^x=27/125

=>(3/5)^x=(3/5)^3

=>x=3

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H9
29 tháng 8 2023 lúc 9:45

b1) \(\left(\dfrac{1}{2}\right)^x=\dfrac{1}{32}\)

\(\Rightarrow\left(\dfrac{1}{2}\right)^x=\left(\dfrac{1}{2}\right)^5\)

\(\Rightarrow x=5\)

b2) \(\dfrac{343}{125}=\left(\dfrac{7}{5}\right)^x\)

\(\Rightarrow\left(\dfrac{7}{5}\right)^3=\left(\dfrac{7}{5}\right)^x\)

\(\Rightarrow x=3\)

b3) \(\left(-\dfrac{3}{2}\right)^x=\dfrac{9}{4}\)

\(\Rightarrow\left(-\dfrac{3}{2}\right)^x=\left(-\dfrac{3}{2}\right)^2\)

\(\Rightarrow x=2\)

b4) \(\left(-\dfrac{2}{3}\right)^x=-\dfrac{8}{27}\)

\(\Rightarrow\left(-\dfrac{2}{3}\right)^x=\left(-\dfrac{2}{3}\right)^3\)

\(\Rightarrow x=3\)

b5) \(\left(\dfrac{3}{5}\right)^x+\dfrac{98}{125}=1\)

\(\Rightarrow\left(\dfrac{3}{5}\right)^x=1-\dfrac{98}{125}\)

\(\Rightarrow\left(\dfrac{3}{5}\right)^x=\dfrac{27}{125}\)

\(\Rightarrow\left(\dfrac{3}{5}\right)^x=\left(\dfrac{3}{5}\right)^3\)

\(\Rightarrow x=3\)

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KL
29 tháng 8 2023 lúc 10:08

a) \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\)

\(x+\dfrac{1}{2}=\dfrac{1}{4}\) hoặc \(x+\dfrac{1}{2}=-\dfrac{1}{4}\)

*) \(x+\dfrac{1}{2}=\dfrac{1}{4}\)

\(x=\dfrac{1}{4}-\dfrac{1}{2}\)

\(x=-\dfrac{1}{2}\)

*) \(x+\dfrac{1}{2}=-\dfrac{1}{4}\)

\(x=-\dfrac{1}{4}-\dfrac{1}{2}\)

\(x=-\dfrac{3}{4}\)

Vậy \(x=-\dfrac{3}{4};x=-\dfrac{1}{2}\)

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a) \(\left(\dfrac{3}{4}-7x\right)^2=\dfrac{1}{4}\)

\(\dfrac{3}{4}-7x=\dfrac{1}{2}\) hoặc \(\dfrac{3}{4}-7x=-\dfrac{1}{2}\)

*) \(\dfrac{3}{4}-7x=\dfrac{1}{2}\)

\(7x=\dfrac{3}{4}-\dfrac{1}{2}\)

\(7x=\dfrac{1}{4}\)

\(x=\dfrac{1}{4}:7\)

\(x=\dfrac{1}{28}\)

*) \(\dfrac{3}{4}-7x=-\dfrac{1}{2}\)

\(7x=\dfrac{3}{4}+\dfrac{1}{2}\)

\(7x=\dfrac{5}{4}\)

\(x=\dfrac{5}{4}:7\)

\(x=\dfrac{5}{28}\)

Vậy \(x=\dfrac{1}{28};x=\dfrac{5}{28}\)

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a) \(\left(x-\dfrac{5}{6}\right)^2=\dfrac{1}{36}\)

\(x-\dfrac{5}{6}=\dfrac{1}{6}\) hoặc \(x-\dfrac{5}{6}=-\dfrac{1}{6}\)

*) \(x-\dfrac{5}{6}=\dfrac{1}{6}\)

\(x=\dfrac{1}{6}+\dfrac{5}{6}\)

\(x=1\)

*) \(x-\dfrac{5}{6}=-\dfrac{1}{6}\)

\(x=-\dfrac{1}{6}+\dfrac{5}{6}\)

\(x=\dfrac{2}{3}\)

Vậy \(x=\dfrac{2}{3};x=1\)

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a) \(\left(1-\dfrac{2}{3}x\right)^2=\dfrac{4}{9}\)

\(1-\dfrac{2}{3}x=\dfrac{2}{3}\) hoặc \(1-\dfrac{2}{3}x=-\dfrac{2}{3}\)

*) \(1-\dfrac{2}{3}x=\dfrac{2}{3}\)

\(\dfrac{2}{3}x=1-\dfrac{2}{3}\)

\(\dfrac{2}{3}x=\dfrac{1}{3}\)

\(x=\dfrac{1}{3}:\dfrac{2}{3}\)

\(x=\dfrac{1}{2}\)

*) \(1-\dfrac{2}{3}x=-\dfrac{2}{3}\)

\(\dfrac{2}{3}x=1+\dfrac{2}{3}\)

\(\dfrac{2}{3}x=\dfrac{5}{3}\)

\(x=\dfrac{5}{3}:\dfrac{2}{3}\)

\(x=\dfrac{5}{2}\)

Vậy \(x=\dfrac{1}{2};x=\dfrac{5}{2}\)

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*) \(\left(\dfrac{2}{3}-x\right)^2=1:\dfrac{4}{9}\)

\(\left(\dfrac{2}{3}-x\right)^2=\dfrac{9}{4}\)

\(\dfrac{2}{3}-x=\dfrac{3}{2}\) hoặc \(\dfrac{2}{3}-x=-\dfrac{3}{2}\)

*) \(\dfrac{2}{3}-x=\dfrac{3}{2}\)

\(x=\dfrac{2}{3}-\dfrac{3}{2}\)

\(x=-\dfrac{5}{6}\)

*) \(\dfrac{2}{3}-x=-\dfrac{3}{2}\)

\(x=\dfrac{2}{3}+\dfrac{3}{2}\)

\(x=\dfrac{13}{6}\)

Vậy \(x=-\dfrac{5}{6};x=\dfrac{13}{6}\)

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KL
29 tháng 8 2023 lúc 10:17

c) \(5^{x+1}-5^x=20\)

\(5^x.\left(5-1\right)=20\)

\(5^x.4=20\)

\(5^x=20:4\)

\(5^x=5\)

\(x=1\)

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c) \(2^x+2^{x+4}=544\)

\(2^x.\left(1+2^4\right)=544\)

\(2^x.17=544\)

\(2^x=544:17\)

\(2^x=32\)

\(2^x=2^5\)

\(x=5\)

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c) \(4^{2x+1}+4^{2x}=80\)

\(4^{2x}.\left(4+1\right)=80\)

\(4^{2x}.5=80\)

\(4^{2x}=80:5\)

\(4^{2x}=16\)

\(4^{2x}=4^2\)

\(2x=2\)

\(x=1\)

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