17.4 指数方程式 Exponential Equations - 独中课程 | 线上补习

高中一 | 高级数学

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17.4 Exponential Equations 指数方程式

Solve the following equations :
解下列方程式：

(1)

$8^{x^2}$ = $64^{6-2x}$

Answer:

–6, 2

(2)

5 $^{x + 1}$ + 5 $^{-x}$ = 6

Answer:

0, –1

(3)

3 $^{x + 1}$ + 9x– 18 = 0

Answer:

(4)

2 $^{2x + 3}$ – 57 = 65(2 $^x$ – 1)

Answer:

x = $\pm$ 3

(5)

3 $^{3x - 1}$ + 9 $^{x + 1}$ = 33 $^{x + 1}$ + 9 $^{x- 1}$

Answer:

1.096

(6)

2(4 $^x$ + 4 $^{-x}$ + (2 $^x$ + 2 $^{-x}$ ) = 6

Answer:

(7)

5 $^x$ = 10 $^{2x - 1}$

Answer:

0.769

(8)

3 $^{x + 1}$ = 4 $^{2x - 1}$

Answer:

1.48

(9)

6 $^x$ = 3 $^{2x - 1}$

Answer:

2.712

(10)

$(x^2-6x+6)^{x^2-7x+12}=1$

Answer:

1, 3, 4, 5

(11)

$(x^2+6x-6)^{x^2-4x+3}=1$

Answer:

1, 3, –7

Exercise Files

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