指數定律的問題,請幫忙

2009-09-23 4:27 am
1.把(5^n+3)-(5^n+1)-(5^n)表示成5的指數
2.解方程
a.(5^n+3)-(5^n+1)-(5^n)=244

b.(8^1+y)(4^2y)=(16^2y)


(請列出計算步驟)


謝謝

回答 (1)

2009-09-23 4:48 am
✔ 最佳答案
1.把(5^n+3)-(5^n+1)-(5^n)表示成5的指數
=(5^n)*5^3 - (5^n)*5 - 5^n
=(5^n)(5^3 - 5 - 1)
= 119(5^n)
2.解方程
a.(5^n+3)-(5^n+1)-(5^n)=244
由 1 )
119(5^n) = 244
5^n = 244/119
log 5^n = log 244/119
n log 5 = log 244/119
n = (log 244/119) / log 5
n = 0.446146276

b.(8^1+y)(4^2y)=(16^2y)
[8^(1+y)] (4^2y) = 16^2y
[2^3(1+y)] [2^2(2y)] = 2^4(2y)
2 ^ [3(1+y) + 2(2y)] = 2 ^4(2y)
3 + 3y + 4y = 8y
y = 3



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