Question

Tìm STN n biết

a) \(\frac{1}{9}.3^4.3^{n+1}=9^4\)

b) \(\frac{1}{2}.2^n+4.2^n=9.2^5\)

Answer 1

Mk làm lun, ko viết lại đề bài nữa nhé =))

a) \(\Leftrightarrow\)\(3^2.3^{n+1}=9^4\)

\(\Leftrightarrow3^{n+1}=9^4:3^2\)

\(\Leftrightarrow3^{n+1}=3^6\)

\(\Rightarrow n+1=6\)

\(\Leftrightarrow n=6-1\)

\(\Rightarrow n=5\)

b)\(\Leftrightarrow2^n.\left(\frac{1}{2}+4\right)=9.2^5\)

\(\Leftrightarrow2^n.\frac{9}{2}=9.2^5\)

\(\Rightarrow2^n=\left(9.2^5\right):\frac{9}{2}\)

\(\Rightarrow2^n=468:\frac{9}{2}\)

Tự tính nốt KQ giúp mk nha ♥

Answer 2

a)1/9*3⁴*3ⁿ⁺¹=9⁴

3⁴*3ⁿ⁺¹ =9⁴/(1/9)=9⁴*9=9⁵

3⁴*3ⁿ⁺¹=3⁴⁺ⁿ⁺¹=9⁵=(3²)⁵=3¹⁰

=>4+n+1=10

n=10-4-1

Vậy n=5

b)1/2*2ⁿ+4*2ⁿ=9*2⁵

2ⁿ*(1/2+4)=9*2⁵

2ⁿ*4.5=9*2⁵

2ⁿ=9*2⁵/4.5=2⁵*2=2⁶

=> Vậy n=6

Answer 3

\(a)\frac{1}{9}.3^4.3^{n+1}=9^4\)

\(\Rightarrow3^{-2}.3^4.3^{n+1}=3^8\)

\(\Rightarrow3^{-2+4+n+1}=3^{n+3}=3^8\)

\(\Rightarrow n+3=8\Rightarrow n=5\)

\(b)\frac{1}{2}.2^n+4.2^n=9.2^5\)

\(\Rightarrow2^n\left(\frac{1}{2}+4\right)=9.2^5\)

\(\Rightarrow2^n.\frac{9}{2}=9.2^5\Rightarrow2^n=9.2^5.\frac{2}{9}=\frac{9.2^5.2}{9}=2^6\)

\(\Rightarrow n=6\)