中四指數及對數函數

1.(3√x)8
= (x8)1/3
= x8/3
由於3√x = x1/3

2.(16/81)3/4
= [(16/81)1/4]3
= [(24/34)1/4]3
= (24/4/34/4)3
= (2/3)3
= 8/27

3.(m-4 n-3/m3 n4)-1
= (m4 n3/m-3 n-4)
= m4-(-3) n3-(-4)
= m4+3 n3+4
= m7 n7

4)8x/3 = 16
23(x/3) = 24
2x = 24
x = 4

5)3x+2﹣3x = 8
32(3x)﹣3x = 8
9(3x)﹣3x = 8
8(3x) = 8
3x = 1
3x = 30
x = 0

6)22x﹣3(2x)+2 = 0
(2x)2﹣3(2x)+2 = 0
設y = 2x
y2﹣3y+2 = 0
(y﹣1)(y﹣2) = 0
y = 1 或 y = 2
2x = 1 或 2x = 2
2x = 20 或 2x = 21
x = 0 或 x = 1

7)3x+y = 27 ---(1)
43x-y = 4 ---(2)
從(1)，
3x+y = 33
x+y = 3 ---(3)
從(2)，
43x-y = 41
3x﹣y = 1 ---(4)
(3)+(4)：
4x = 4
x = 1 ---(5)
將(5)代入(3)，
1+y = 3
y = 2
∴x = 1，y = 2

1. x^(8/3)
2.16/81=(2^4)/(3^4)
(16/81)^3/4 = (2^3)/(3^3)=8/27
3 m^7 n^7
4 8^x/3=16
2^(3x/3) = 2^4
x=4
5. 3 ^x+2-3^x=8
9(3^x)-3^x = 8
8(3^x) = 8
x=0

6. (2^x)^2 -3(2^x)+2=0
(2^x - 1)(2^x -2) =0
x=0 or 1

7 summing up

3^x + 2^6x = 31
take logarithm
ln 3^x + ln 2^6x =ln31
x ln 3 + x ln 2^6 = ln31
x= ln 31 / (ln3+ln64)=0.65316029
y= 24.95055316