Đáp án+Giải thích các bước giải:
bài `1`
`a) 5 . 5^2 . 5^7`
`= 5^1 . 5^2 . 5^7`
`= 5^10`
`b) 3. 5 . 15 . 15^3`
`= 15^1 . 15^1 . 15^3`
`= 15^5`
`c) 2^15 : 2^11`
= 2^4 `
`d) 11^300 : 11^200`
`= 11^100`
`e) a . a^2 . a^5`
`= a^1 . a^2 . a^5`
`= a^8`
`g) x^10 . x^20 . x^30`
`= x^60`
`h) m^10 : m`
`= m^15 : m^1`
`= m^14`
`k) 2^1 . 2^2 . 2^x + 1`
`= 2^1 . 2^2 . 2^x . 2^1`
`= 2^4 . 2^x`
`= 2^x + 4 `
bài `2`
`a) x^2 = 16`
`⇒x = 4 `
` b) x^2 = 81`
`⇒x=9`
`c) ( x - 3 )^2 = 81`
`⇒ ( x - 3 )^2 = 9^2 `
`⇒ x - 3 = 9 `
`⇒ x = 6 `
`d) ( x + 1 )^3 = 125`
`( x + 1 )^3 = 5^3`
`x + 1= 5`
`x= 4`
`e) ( 7 - x )^3 = 216`
`(7 - x )^3 = 6^3`
` 7 - x= 6`
`x = 1`
`g) ( 2x - 1 )^2 = 49`
`( 2x - 1 )^2 = 7^2`
`2x -1 = 7`
`2x= 6`
`x = 3`
`h) 2^x = 8`
`2^x = 2^3 `
`x= 3`
`k) 3^x - 1 = 243 `
`3^x - 3^1 = 3^5`
`3^x = 3^4`
`x = 4`
Bài `3 : `
`a) 5 . 5^x+1 = 625 `
`5^1 . 5^x . 5^1 = 625 `
`5^x . 5^2 = 625 `
`5^x = 625 : 5^2 `
`5^x = 5^2 `
`x = 2 `
`b) 2^x . 2^x - 2^1 = 32`
`2^x . 2^x - 2^1 = 2^5`
`2^x . 2^x = 2^4`
`2^x = 2^2`
`x = 2 `
`c) 2^x + 2^x + 2^1 = 48 `
`2^x + 2^x + 2^1 = 2^5 + 2^4 `
`2^x + 2^x = 2^4 + 2^4`
`2^x = 2^4`
`x = 4 `
`d) 7^x + 7^x+2 = 2450`
`7x + 7x+2 = 2450`
`⇒ 7x( 1 + 72 ) = 2450`
`⇒ 7x . 50 = 2450`
`⇒ 7x = 49`
`⇒ 7x = 72`
`e)`3^(x+1)+3^(x+2)=324`
`⇔3^(x).3^1+3^(x).3^2=324`
`⇔3^x(3+3^2)=324`
`⇔3^(x).12=324`
`⇔3^x=324:12`
`⇔3^x=27`
`⇔3^x=3^3`
`⇔x=3`
Vậy `x=3`
