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第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

第十三章: 方程组 Simultaneous Equations

第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming

17.4 指数方程式 Exponential Equations

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:
1
(4)

2^{2x + 3} – 57 = 65(2^x – 1)

Answer:
x = \pm3
(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:
0
(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