Question

1/ Chứng minh

a)7^6 + 7^5 - 7^4 chia hết 55

b)16^5 + 2^5 chia hết 33

c)81^7 - 27^9 - 9^13 chia hết 405

2/ Tìm x

a)5^x + 5^x+2 = 650

b)3^x+1 + 5 x 3^x+1 = 162

Giải giúp mình nha mn

Answer 1

\(7^6+7^5-7^4\)

\(=7^4\left(7^2+7-1\right)\)

\(=7^4\cdot55⋮55\)

Answer 2

\(16^5+2^5\)

\(=\left(2^4\right)^5+2^5\)

\(=2^{20}+2^5\)

\(=2^5\left(2^{15}+1\right)\)

\(=2^5\cdot32769⋮33\)

Answer 3

\(81^7-27^9-9^{13}\)

\(=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)

\(=3^{28}-3^{27}-3^{26}\)

\(=3^{26}\left(3^2-3-1\right)\)

\(=3^{26}\cdot5\)

\(=3^{22}\cdot405⋮405\)

Answer 4

\(5^x+5^{x+2}=650\)

\(\Leftrightarrow5^x\left(1+5^2\right)=650\)

\(\Leftrightarrow5^x\cdot26=650\)

\(\Leftrightarrow5^x=25\)

\(\Leftrightarrow x=2\)

Answer 5

Bạn viết lại đề câu b cho rõ ràng tí nha.Mik ko hiểu đề cho lắm,

Chúc bạn học tốt~

Answer 6

b) 3^x+1 + 5 . 3^x+1 = 162

Answer 7

\(3^{x+1}+5\cdot3^{x+1}=162\)

\(\Leftrightarrow3^{x+1}\left(1+5\right)=162\)

\(\Leftrightarrow3^{x+1}=27\)

\(\Leftrightarrow x=2\)