math,,,,,,,,,,,,,(F.4)

1.let y=6^x

36y-2(6y)-12y=2
12y=2
y=1/6
6^x=1/6
x=-1

2.let y=2^2x

y^2-20y+64=0
(y-16)(y-4)=0
y=16 or4
2^2x=16 or4
2x=4 or2
x=2 or1

3.log(100root10) -log(10root10)=(1/10)log100-(1/10)log10
=(1/5)-(1/10)=1/10

4.log5+2log2-1 / 2log4-log0.5=log5+log4-log10/4log2-(-1)log2
=log2/5log2=1/5

5.4^2x =6^3x-1
log16^x=log6^3x-1
xlog16=(3x-1)log6
=3xlog6-log6
x(3log6-log16)=log6
x=0.688,cor. to 3 sig. fig.

2007-02-04 19:14:11 補充：
3 is wrong log(100root10) -log(10root10)=log100 log√10-log10-log√10=2-1=1

1)
6^x+2 -2(6^x+1) - 12(6^x) =2

6^x [6^2 - 2(6) - 12] = 2

6^x (12) = 2

6^x = 1/6

6^x = 6^(-1)

x = -1


2)
2^4x - 20(2^2x) +64 = 0

(2^2x - 16)(2^2x - 4) = 0

2^2x = 16 or 2^2x = 4

2^2x = 2^4 or 2^2x = 2^2

2x = 4 or 2x = 2

x =2 or x =1


3)
log(100√10) -log(10√10)

= log 100 + log√10 - log 10 - log√10

= log 100 - log 10

= 2 - 1

= 1


4)
log5+2log2-1 / 2log4-log0.5

=( log 5 + log4 - log 10) / (log 16 - log 0.5)

= (log20 - log10) / (log32)

= log2 / log32

= log2 / (log2^5)

= log2/(5log2)

= 1/5


5)
4^2x = 6^3x-1

x log 16 = (3x -1) log6

x log 16 = 3x log6 - log6

(3log6 - log16) x= log6

x = log6/(3log6 - log16)

by calculator

x = 0.688426084

hence,the answer is 0.688(correct to 3 decimal numbers)