Question

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

Tìm x thuộc Q

A) \(\frac{x}{12}\)= \(\frac{-1}{4}\) B) \(\left(\frac{1}{3}\right)\)^2x-1   = \(\frac{1}{243}\)         C) \(\frac{4}{7}\).x - \(\frac{2}{3}\)= \(\frac{1}{5}\)

So Sánh 5²⁰² và 2⁵⁰⁵

Answer 1

a/b=x/y (=) a.y=b.x

A= x/12= (-1)/4

=) x.4=(-1).12

=)x.4=(-12)

=)x.=(-12);4

=)x=(-3)

Answer 2

a/b=x/y       <=>a.y=b.x

a,=>x.4=12.-1      

=>x.4=-12

=>x=-3

b,(1/3)^2x-1=1/243

=>(1/3)^2x-1=(1/3^5)

=>2x-1=1

=>2x=2

=>x=1

c,4/7.x-2/3=1/5

=>4/7x=13/15

=>x=13/15:4/7

=>x=91/60

 

Answer 3

(1/3)^2x-1=1/243

=)(1/3)^2x-1=(1/3)⁵

=)2x-1=5

=)2x=6

=)x=3

4/7.x-2/3=1/5

=)4/7.x=13/15

=)x=91/60

5²⁰²  và 2⁵⁰⁵

= (5²)¹⁰¹ và (2⁵)¹⁰¹

=25¹⁰¹ và 32¹⁰¹ 

Vì 25<32=)25¹⁰¹<32¹⁰¹

Vậy 5²⁰²<2⁵⁰⁵

Answer 4

Câu 1 : \(\frac{a}{b}=\frac{x}{y}\) khi \(a.y=bx\)

Câu 2 : 

a) \(\frac{x}{12}=\frac{-1}{4}\Rightarrow x.4=-12\Rightarrow x=-12:4=-3\)

b) \(\left(\frac{1}{3}\right)^{2x-1}=\frac{1}{243}\)\(\Rightarrow\left(\frac{1}{3}\right)^{2x-1}=\left(\frac{1}{3}\right)^5\Rightarrow2x-1=5\Rightarrow2x=6\Rightarrow x=3\)

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

     \(\frac{4}{7}.x=\frac{1}{5}+\frac{2}{3}=\frac{13}{15}\)

      \(x=\frac{13}{15}:\frac{4}{7}=\frac{91}{60}\)

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

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

Vì 25 < 32 nên 25¹⁰¹ < 32¹⁰¹ hay 5²⁰² < 2⁵⁰⁵