Question

[Cao Hồng Ngọc]

Tìm số tự nhiên n biết :
a) 2^n = 8
b) 5^n+1 = 125
c) 3.2^n-2
d) 2.7^n-1 +3 = 101
e) 3.5^2n+1 -6^2 = 339
Nhanh ạ em đang cần gấp ạ !!

Answer 1

[HT.Phong (9A5)]

a) \(2^n=8\)

\(\Rightarrow2^n=2^3\)

\(\Rightarrow n=3\)

b) \(5^{n+1}=125\)

\(\Rightarrow5^{n+1}=5^3\)

\(\Rightarrow n+1=3\)

\(\Rightarrow n=3-1=2\)

c) Mình không rõ đề:

d) \(2\cdot7^{n-1}+3=101\)

\(\Rightarrow2\cdot7^{n-1}=101-3\)

\(\Rightarrow2\cdot7^{n-1}=98\)

\(\Rightarrow7^{n-1}=\dfrac{98}{2}\)

\(\Rightarrow7^{n-1}=49\)

\(\Rightarrow7^{n-1}=7^2\)

\(\Rightarrow n-1=2\)

\(\Rightarrow n=1+2=3\)

e) \(3\cdot5^{2n+1}-6^2=339\)

\(\Rightarrow3\cdot5^{2n+1}=339+36\)

\(\Rightarrow3\cdot5^{2n+1}=375\)

\(\Rightarrow5^{2n+1}=125\)

\(\Rightarrow5^{2n+1}=5^3\)

\(\Rightarrow2n+1=3\)

\(\Rightarrow2n=2\)

\(\Rightarrow n=\dfrac{2}{2}=1\)