1/ a) $2^{x+3}$ + $2^{x}$ = 144
b) $2^{2x + 5}$ + $2^{2x + 1}$ = 136
2/Viết tích thương sau dưới dạng lũy thừa
a) $3^{2}$.81.27
b) $8^{4}$÷$2^{5}$
3/Tìm n∈N biết
a) $2^{n}$=64
b)7. $7^{n+1}$=78
c)$(4.x+7)^{12}$ =1
d)$(2.x-1)^{4}$ =81
e) $5^{x+3}$-$5^{x}$=3100
1/ a) $2^{x+3}$ + $2^{x}$ = 144 b) $2^{2x + 5}$ + $2^{2x + 1}$ = 136 2/Viết tích thương sau dưới dạng lũy thừa a) $3^{2}$.81.27 b) $8^{4}$÷$2
By Samantha
`1)`
`a) 2^(x + 3) + 2^x = 144`
`2^x. 2^3 + 2^x = 144`
`2^x. (2^3 + 1) = 144`
`2^x. 9 = 144`
`2^x = 144 : 9`
`2^x = 16`
`2^x = 2^4`
`=> x = 4`
`b) 2^(2x + 5) + 2^(2x + 1) = 136`
`2^(2x ). 2^5 + 2^(2x). 2^1 = 136`
`2^(2x). (2^5 + 2^1) = 136`
`2^(2x). (32 + 2) = 136`
`2^(2x). 34 = 136`
`2^(2x) = 136 : 34`
`2^(2x) = 4`
`2^(2x) = 2^2`
`=> 2x = 2`
`=> x = 2 : 2`
`=> x = 1`
`2)`
`a) 3^2. 81. 27`
`= 3^2. 3^4. 3^3`
`= 3^9`
`b) 8^4 : 2^5`
`= (2^3)^4 : 2^5`
`= 2^12 : 2^5`
`= 2^7`
`3)`
`a) 2^n = 64`
`2^n = 2^6`
`=> n = 6`
`b) 7. 7^(n+ 1) = 78`
– Vì `78` không`vdots 7`
`=> x ∈ ∅`
`c) (4x + 7)^12 = 1`
`(4x + 7)^12 = 1^12`
`=> 4x + 7 = 1`
– Vì `1 < 7`
`=> x ∈ ∅`
`d) (2x – 1)^4 = 81`
`(2x – 1)^4 = 3^4`
`=> 2x – 1 = 3`
`=> 2x = 3 + 1`
`=> 2x = 4`
`=> x = 4 : 2`
`=> x = 2`
`e) 5^(x + 3) – 5^x = 3100`
`5^x. 5^3 – 5^x = 3100`
`5^x. (5^3 – 1) = 3100`
`5^x. (125 – 1) = 3100`
`5^x. 124 = 3100`
`5^x = 3100 : 124`
`5^x = 25`
`5^x = 5^2`
`=> x = 2`