1)試舉出一組a和b的可能值(a不等於b),使loga對底數為8乘logb對底數為8=1
2)已知log10對底數為25=x,試以x表示log2對底數為5.
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2011-11-27 1:39 am
回答 (3)
2011-11-27 2:53 am
✔ 最佳答案
1)log₈ a+log₈ b=1 log₈(ab)=1 8¹=abab=8 So, a & b ≠0, a can be any no. which b=8/a. 2) log₂₅10=xlog_(5²)10=xlog₅10=2xlog₅(2×5)=2xlog₅2+log₅5=2xlog₅2+1=2x2x-1=log₅2
參考: Hope I Can Help You ! ^_^ ( From Me )
2011-11-27 5:32 am
remember log10 100 = 2 => 10^2 = 100
loga b = c => a^c = b
1.
log8 a x log8 b = 1
log8 (ab) = log8 8
ab = 8
2.
log25 10 = x
log25 10 = x log25 25 (or directly to 10 = 25^x)
log25 10 = log25 (25^x)
10 = 25^x = 5^2x
log5 10 = log5 (5^2x)
log5 10 = (2x)log5 (5)
x = (1/2)log5 10
2011-11-26 21:35:02 補充：
2x = log5 (5 x 2)
2x = log5 (5) + log5 (2)
2x = 1 + log5 (2)
2x -1 = log5 (2)
2011-11-27 19:43:10 補充：
1.
a = 8^n
b = 8^(1/n)
loga b = c => a^c = b
1.
log8 a x log8 b = 1
log8 (ab) = log8 8
ab = 8
2.
log25 10 = x
log25 10 = x log25 25 (or directly to 10 = 25^x)
log25 10 = log25 (25^x)
10 = 25^x = 5^2x
log5 10 = log5 (5^2x)
log5 10 = (2x)log5 (5)
x = (1/2)log5 10
2011-11-26 21:35:02 補充：
2x = log5 (5 x 2)
2x = log5 (5) + log5 (2)
2x = 1 + log5 (2)
2x -1 = log5 (2)
2011-11-27 19:43:10 補充：
1.
a = 8^n
b = 8^(1/n)
2011-11-27 3:43 am
1)
(log8a)(log₈ b)=1
(loga)(logb)/(log8)^2 =1
(loga)(logb)=(log2^3)^2
(loga)(logb)=9(log2)(log2)
=>loga=9log2 ---------1
logb=log2-------------2
=>a=2^9 b=2
2)log2510 =x
log510/log55^2 =X
log5(2X5)/log55^2 =X
(log52+1) /2 =X
=> log52=2X-1
(log8a)(log₈ b)=1
(loga)(logb)/(log8)^2 =1
(loga)(logb)=(log2^3)^2
(loga)(logb)=9(log2)(log2)
=>loga=9log2 ---------1
logb=log2-------------2
=>a=2^9 b=2
2)log2510 =x
log510/log55^2 =X
log5(2X5)/log55^2 =X
(log52+1) /2 =X
=> log52=2X-1
參考: ME
收錄日期: 2021-04-13 18:23:53
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