整數指數定律...急

1.
125^x = 1
125^x = 125^0
x= 0

2.
7^x = 3^x
由於只有兩方同時為一才有解,
7^x = 1
x = 0

3.
7^(x-1)=1
7^(x-1)=7^0
x-1=0
x=1

4.
243^(-x-1) = 3*9
3^(-5x-5) = 27
3^(-5x-5) = 3^3
-5x-5 = 3
x = -8/5

5.
(7^x)(7^2x)=1
7^(2x+x) = 7^0
3x=0
x=0

2010-09-18 13:40:20 補充：
About 002 Jenus 's answers :
3. 7^(x-1) =1
x=2

Check :
7^(2-1) is 7 but not 1.
The answer should be 1

7^(1-1) = 7^0 = 1

1. x=0 (所有數的0次方都等於1)

2. 7^(x) =3^(x) *(when 7的那個x次方等於3的那個x次方)
x=0

3. 7^(x-1) =1
x=2

4. 243^(-x-1) =3^(9)
243^(-x-1) =59049
243^(-x-1) =243^(2)
x =-3

5. 7^(x)*7^(2x) =1
x =0

2010-09-18 13:33:09 補充：
No.4 ( 243^(-x-1) =3^(9) ) I was wrong,
The correct question and answer:
243^(-x-1) = 3*9
3^(-5x-5) = 27
3^(-5x-5) = 3^3
x = -8/5

2010-09-18 13:34:10 補充：
回答者001 笨蛋小子is correct^_^