Question

1) \(\dfrac{a}{b}\) = \(\dfrac{x}{y}\) khi nào???

2) Tìm x ∈ Q, biết a) \(\dfrac{x}{12}\) = \(\dfrac{-1}{4}\)

b) \(\dfrac{1}{3}\)^2x-1 = \(\dfrac{1}{243}\)

c) \(\dfrac{4}{7}\).x -\(\dfrac{2}{3}\)= \(\dfrac{1}{5}\)

3) so sánh 5²⁰² và 2⁵⁰⁵

Answer 1

1,\(\dfrac{a}{b}=\dfrac{x}{y}\) khi ay=bx

2,

a,x=\(\dfrac{-1.12}{4}\)

x=\(\dfrac{-12}{4}=-3\)

b,\(\left(\dfrac{1}{3}\right)^{2x-1}=\left(\dfrac{1}{3}\right)^5\)

\(\Rightarrow\)2x-1=5

2x=6

x=6:2=3

c,\(\dfrac{4}{7}\).x=\(\dfrac{1}{5}+\dfrac{2}{3}\)

\(\dfrac{4}{7}.x=\dfrac{3}{15}+\dfrac{10}{15}\)

\(\dfrac{4}{7}.x=\dfrac{13}{15}\)

\(x=\dfrac{13}{15}:\dfrac{4}{7}\)

x=\(\dfrac{13}{15}.\dfrac{7}{4}=\dfrac{91}{60}\)

3,ta có:\(5^{202}=\left(5^2\right)^{101}\)=\(25^{101}\)

2\(^{505}\)=\(\left(2^5\right)^{101}\)=\(32^{101}\)

vì 25<32 nên \(25^{101}< 32^{101}\) hay \(5^{202}< 2^{505}\)

Answer 2

1) \(\dfrac{a}{b}=\dfrac{x}{y}\) khi \(a.y=b.x\)

2) \(a,\dfrac{x}{12}=\dfrac{-1}{4}\)

\(\Rightarrow4x=-12\)

\(\Rightarrow x=-\dfrac{12}{4}=-3\)

Vậy x = -3

\(b,\left(\dfrac{1}{3}\right)^{2x-1}=\dfrac{1}{243}\)

\(\left(\dfrac{1}{3}\right)^{2x-1}=\left(\dfrac{1}{3}\right)^5\)

\(\Rightarrow2x-1=5\)

\(\Rightarrow x=\dfrac{5-1}{2}=2\)

Vậy x = 2

\(c,\dfrac{4}{7}x-\dfrac{2}{3}=\dfrac{1}{5}\)

\(\dfrac{4}{7}x=\dfrac{1}{5}+\dfrac{2}{3}\)

\(\dfrac{4}{7}x=\dfrac{13}{15}\)

\(\Rightarrow x=\dfrac{13}{15}:\dfrac{4}{7}=1\dfrac{31}{60}\)

Vậy \(x=1\dfrac{31}{60}\)

3) So sánh \(5^{202}\) và \(2^{505}\)

\(5^{202}=\left(5^2\right)^{101}=25^{101}\)

\(2^{505}=\left(2^5\right)^{101}=32^{101}\)

\(\Rightarrow25^{101}< 32^{101}\)

\(\Rightarrow5^{202}< 2^{505}\)