Question

[Sách Giáo Khoa]

Tìm số tự nhiên n bé nhất sau cho :

a) \(\left(\dfrac{1}{2}\right)^n\le10^{-9}\)

b) \(3-\left(\dfrac{7}{5}\right)^n\le0\)

c) \(1-\left(\dfrac{4}{5}\right)^n\ge0,97\)

d) \(\left(1+\dfrac{5}{100}\right)^n\ge2\)

Answer 1

[Mới vô]

a) \(\left(\dfrac{1}{2}\right)^n\le10^{-9}\)\(\Leftrightarrow2^{-n}\le10^{-9}\)\(\Leftrightarrow-n\le log^{10^{-9}}_2\)\(\Leftrightarrow-n\le-9log^{10}_2\)\(\Leftrightarrow n\ge9log^{10}_2\)\(\Leftrightarrow n\ge30\).
Vậy \(n=30\).

b) \(3-\left(\dfrac{7}{5}\right)^n\le0\)

\(\Leftrightarrow-\left(\dfrac{7}{5}\right)^n\le-3\)

\(\Leftrightarrow\left(\dfrac{7}{5}\right)^n\ge3\)\(\Leftrightarrow n\ge log^3_{\dfrac{7}{5}}\)

\(\Rightarrow\)\(n\in\left\{4;5;6;7;...\right\}\Rightarrow n=4\)

c) \(1-\left(\dfrac{4}{5}\right)^n\ge0,97\)

\(\Leftrightarrow-\left(\dfrac{4}{5}\right)^n\ge-0,3\)

\(\Leftrightarrow\left(\dfrac{4}{5}\right)^n\le0,3\)\(\Leftrightarrow n\ge log^{0,3}_{\dfrac{4}{5}}\)

\(\Rightarrow n\in\left\{6;7;8;9...\right\}\Rightarrow n=6\)

d)\(\left(1+\dfrac{5}{100}\right)^n\ge2\)

\(\Leftrightarrow1,05^n\ge2\)

\(\Rightarrow n\in\left\{15;16;17;18;...\right\}\Rightarrow n=15\)

Answer 2

[Mới vô]

em mới lp 6 k biết trình bày kiểu lp 12