Toán tìm x , 5^x × 5^x+1 × 5^x+2 … 5^x+100 = 5^6060 11/07/2021 By Natalia tìm x , 5^x × 5^x+1 × 5^x+2 … 5^x+100 = 5^6060
Đáp án: x = 10 Giải thích các bước giải: $5^{x}$ . $5^{x+1}$ . $5^{x+2}$ ….. $5^{x+100}$ = $5^{6060}$ → $5^{x+x+1+x+2+…..+x+100}$ = $5^{6060}$ → x + x + 1 + x + 2 + ….. + x + 100 = 6060 → ( x + x + x + ….. + x ) + [ ( 100 + 1 ) . 100 : 2 ] = 6060 → 101 . x + 5050 = 6060 → 101 . x = 1010 → x = 10 Trả lời
`5^x. 5^(x + 1). 5^(x + 2) … 5^(x + 100) = 5^6060` `=> 5^(x + (x + 1) + (x + 2) + … + (x + 100)) = 5^6060` `=> 5^((x + x + x + … + x) + (1 + 2 + .. + 100)) = 5^6060` `=> 5^(101x + (1 + 2 + … + 100))= 5^6060` `=> 101x + (1 + 2 + … + 100) = 6060` `=> 101x + (1 + 100) . 100/2 = 6060` `=> 101x + 101 . 50 = 6060` `=> 101. (x + 50) = 6060` `=> x + 50 = 6060 : 101` `=> x + 50 = 60` `=> x = 60 – 50` `=> x = 10` Trả lời
Đáp án: x = 10
Giải thích các bước giải:
$5^{x}$ . $5^{x+1}$ . $5^{x+2}$ ….. $5^{x+100}$ = $5^{6060}$
→ $5^{x+x+1+x+2+…..+x+100}$ = $5^{6060}$
→ x + x + 1 + x + 2 + ….. + x + 100 = 6060
→ ( x + x + x + ….. + x ) + [ ( 100 + 1 ) . 100 : 2 ] = 6060
→ 101 . x + 5050 = 6060
→ 101 . x = 1010
→ x = 10
`5^x. 5^(x + 1). 5^(x + 2) … 5^(x + 100) = 5^6060`
`=> 5^(x + (x + 1) + (x + 2) + … + (x + 100)) = 5^6060`
`=> 5^((x + x + x + … + x) + (1 + 2 + .. + 100)) = 5^6060`
`=> 5^(101x + (1 + 2 + … + 100))= 5^6060`
`=> 101x + (1 + 2 + … + 100) = 6060`
`=> 101x + (1 + 100) . 100/2 = 6060`
`=> 101x + 101 . 50 = 6060`
`=> 101. (x + 50) = 6060`
`=> x + 50 = 6060 : 101`
`=> x + 50 = 60`
`=> x = 60 – 50`
`=> x = 10`