中四log問題2

a) log x=1/3,find x
x = 10^(1/3)
x = 10^(1/3) or 2.1544 (accurate up to 4 decimal place)

b) log 125 5
Let x = log125x
5 = 125^x
5 = (5^3)^x
5^1 = 5^(3x)
1 = 3x
3x = 1
x = 1/3

Check: log 5/ log 125 = 0.69897/2.09691 = 0.3333

c) (log732)^2
(log 32/log 7)^2
(1.5051/0.5451)^2
1.7809^2
3.1719

d) (log6x^4)/(log6x)
4 log6x/log6x
4

e)1/2log(1-x) =1
log (1 – x) = 1/0.5
log (1 – x) = 2
1 - x = 10^2
x = 1 – 10^2
x = 1 – 100
x = - 99

a)log x=1/3,find x
logx=1/3(I think 10 is the base)
10^1/3=x

b)log 125 5
let the answer be "x"
log125 5=x
125^x=5
x=1/4

c)(log732)^2
=(1.78...)^2
=3.17(cor. to 3 sig. fig.)

d)(log6x^4)/(log6x)
=(log6 x^4)/(log6 x)
=(4log6 x)/(log6 x)
=4
e)1/2log(1-x)=1
log(1-x)=2
1-x=10^2
x=-99



2011-03-09 13:36:15 補充：
Sorry,something wrong in b)
It should be:
b)log 125 5
let the answer be "x"
log125 5=x
125^x=5
x=1/3