f.4既數學,help,(20點)

(1) [log(4x^2)+log√(2x)] / log(2x)
= [log(2x)^2+log√(2x)] / log(2x)
= [2log(2x) + (1/2)log(2x)] / log(2x)
= 2.5log(2x) / log(2x)
= 2.5
(2) a = log 5
(a) log√125
= log√5^3
= log5^(3/2)
= (3/2)log5
= 3a/2
(b) log(1/50)
= log1 - log(5*10)
= 0 - log5 - log10
= -a - 1
(c) log(1/√5)
= log1 - log√5
= 0 - (1/2)log5
= -0.5a
(d) log20
= log(100/5)
= log100 - log5
= 2 - a
3. log3=x及log4=y
log(1/48)
= log1 - log(3*4*4)
= 0 - log3 - log4 - log4
= -x - 2y
4. [log(1/x) - logx] / log√x
= [log1 - logx - logx] / [(1/2)logx]
= -2logx / [(1/2)logx]
= -4
5. (log5+2log2-1) / (log16-log0.5)
= (log5 + log4 - log10) / [log(16/0.5)]
= log(5*4/10) / log(32)
= log2 / log(2^5)
= log2 / 5log2
= 1/5
6. (2-log8-3log5) / (2log5-log0.25)
= (log100 - log8 - log5^3) / (log5^2 - log0.25)
= log(100/8/125) / log (25/0.25)
= log(0.1) / log(100)
= -1/2
7. log3=x及log5=y
(a) log108
= log(27 * 4)
= log27 + log100/25
= log3^3 + log100 - log5^2
= 3log3 + 2 - 2log5
= 3x - 2y + 2
(b) log√180
= (1/2)log180
= (1/2)log(3^2 * 100 / 5)
= (1/2)[2log(3) + log100 - log5]
= (1/2)(2x + 2 - y)
= x + 1 - 0.5y

這裏可以幫到你
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