Bài 6: Lũy thừa của một số hữu tỉ (tiếp theo...)

\(3^{-2}.2^x+2^x.3=\dfrac{7}{36}\)

\(=>2^x\left(\dfrac{1}{9}+3\right)=\dfrac{7}{36}\)

\(=>2^x.\dfrac{28}{9}=\dfrac{7}{36}\)

\(=>2^x=\dfrac{1}{16}\)

\(=>2^x=2^{-4}\)

\(=>x=-4\)

\(=-\dfrac{5}{7}\left(16+\dfrac{1}{3}+23+\dfrac{2}{3}\right)\)

\(=\dfrac{-5}{7}\cdot40=-\dfrac{200}{7}\)

\(-\dfrac{5}{7}.16\dfrac{1}{3}+\dfrac{5}{7}.\left(-23\dfrac{2}{3}\right)\)

\(=\dfrac{-5}{7}.16\dfrac{1}{3}+\dfrac{-5}{7}.23\dfrac{2}{3}\)

\(=-\dfrac{5}{7}.\left(16\dfrac{1}{3}+23\dfrac{2}{3}\right)\)

\(=-\dfrac{5}{7}.40\)

\(=\dfrac{-200}{7}\)

\(=\dfrac{2^{14}}{2^6}\cdot\dfrac{3^6}{3^9}=\dfrac{2^8}{3^3}\)

256/27

x= (-9/5):(-5/9)

x = -1/1

x = -1

x = -1

=>2x+1=7

=>2x=6

=>x=3

2^2x+1=2⁷

2x+1=7

2x=7-1

2x=6

x=6:2

x=3

x = 3

a) \(A=\dfrac{2^6\cdot9^2}{6^4\cdot8}\)

\(=\dfrac{2^6\cdot\left(3^2\right)^2}{3^4\cdot2^4\cdot2^3}\)

\(=\dfrac{2^6\cdot3^4}{3^4\cdot2^7}\)

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

b) \(B=\dfrac{2^{13}\cdot3^7}{2^{15}\cdot3^2\cdot9^2}\)

\(=\dfrac{2^{13}\cdot3^7}{2^{15}\cdot3^2\cdot\left(3^2\right)^2}\)

\(=\dfrac{2^{13}\cdot3^7}{2^{15}\cdot3^6}\)

\(=\dfrac{3}{2^2}\)

\(=\dfrac{3}{4}\)

\(A=\dfrac{2^6.9^2}{6^4.8}=\dfrac{2^6.3^4}{2^7.3^4}=\dfrac{1}{2}\)

\(B=\dfrac{2^{13}.3^7}{2^{15}.3^2.9^2}=\dfrac{3^7}{2^2.3^6}=\dfrac{3}{4}\)

\(\left(-x\right)^8:x^2\)

\(=x^8:x^2\)

\(=x^{8-2}\)

\(=x^6\)

_____

\(27^8:9^4\)

\(=\left(3^3\right)^8:\left(3^2\right)^4\)

\(=3^{24}:3^8\)

\(=3^{24-8}\)

\(=3^{16}\)

\(\left(\dfrac{1}{2}-\dfrac{1}{3}\right)\cdot6^x\cdot6^{x+2}=6^{15}\)

\(\Rightarrow\dfrac{1}{6}\cdot6^{x+2+x}=6^{15}\)

\(\Rightarrow6^{2x+3}=6^{15}:\dfrac{1}{6}\)

\(\Rightarrow6^{2x+2}=6^{16}\)

\(\Rightarrow2x+2=16\)

\(\Rightarrow2x=16-2\)

\(\Rightarrow2x=14\)

\(\Rightarrow x=7\)

1/6 . 6^x . 6^x.6²=6¹⁵

             6^x+2.6=6¹⁵

             6^2x     = 6¹⁵/6

             6^2x     =6¹⁴

         =>2x      = 14

        =>x         = 14:2

        =>x         = 7

help tui

\(27< 3^n< 3\cdot81\)

\(\Rightarrow3^3< 3^n< 3\cdot3^4\)

\(\Rightarrow3^3< 3^n< 3^5\)

\(\Rightarrow3< n< 5\)

\(\Rightarrow n=4\) (với \(3^n\in N^+\))

=>3³<3ⁿ<3¹.3⁴

=>3³<3ⁿ<3⁵

=>n = 4