Câu hỏi của Nguyễn Văn Hoàn

Question

$2^{x+2}$-$2^x$= 96

CHỨNG MINH RẰNG:

$10^6$- $5^7$$⋮$59

$81^7$-$27^9$-

Chu Công Đức · Accepted Answer

a) $2^{x+2}-2^x=96$$\Leftrightarrow2^x.4-2^x=96$

$\Leftrightarrow2^x\left(4-1\right)=96$$\Leftrightarrow2^x.3=96$$\Leftrightarrow2^x=32=2^5$

$\Leftrightarrow x=5$

Vậy $x=5$

b) $10^6-5^7=\left(2.5\right)^6-5^{6+1}=2^6.5^6-5^6.5=5^6\left(2^6-5\right)=5^6\left(64-5\right)=5^6.59⋮59$

c) $81^7-27^9-9^{13}=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}=3^{28}-3^{27}-3^{26}$

$=3^{24}\left(3^4-3^3-3^2\right)=3^{24}\left(81-27-9\right)=3^{24}.45⋮45$

Câu trả lời:

a) $2^{x+2}-2^x=96$$\Leftrightarrow2^x.4-2^x=96$

$\Leftrightarrow2^x\left(4-1\right)=96$$\Leftrightarrow2^x.3=96$$\Leftrightarrow2^x=32=2^5$

$\Leftrightarrow x=5$

Vậy $x=5$

b) $10^6-5^7=\left(2.5\right)^6-5^{6+1}=2^6.5^6-5^6.5=5^6\left(2^6-5\right)=5^6\left(64-5\right)=5^6.59⋮59$

c) $81^7-27^9-9^{13}=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}=3^{28}-3^{27}-3^{26}$

$=3^{24}\left(3^4-3^3-3^2\right)=3^{24}\left(81-27-9\right)=3^{24}.45⋮45$

Edogawa Conan · Answer

1. Ta có: 2^{x + 2} - 2^x = 96

=> 2^x.4 - 2^x = 96

=> 2^x(4 - 1) = 96

=> 2^x = 96 : 3

=> 2^x = 32

=> 2^x = 2⁵

=> x = 5

2. Ta có: 10⁶ - 5⁷ = (2.5)⁶ - 5⁷ = 2⁶.5⁶ - 5⁶.5 = 5⁶(64 - 5) = 5⁶ . 59 $⋮$59

81⁷ - 27⁹ - 9¹³ = (3⁴)⁷ - (3³)⁹ - (3²)¹³ = 3²⁸ - 3²⁷ - 3²⁶ = 3²⁴.(3⁴ - 3³ - 3²) = 2²⁴. 45 $⋮$45