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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

17.2 对数 Logarithm

17.2 Logarithm 对数


 

1. Simplify 化简
(a) {log}_3{\sqrt[3]{81\sqrt[4]{729\times9^{2/3}}}}

(b) 2log{\frac{9}{35}}log{\frac{32}{525}} + log{\frac{224}{243}}

(c) log25 + log2\cdotlog50 + (log2)^2

Answer:
(a) \frac{35}{18}

(b) 0

(c) 2

2.

If a^2 + b^2 = 14ab, prove that log{\frac{a+b}{4}} = \frac{1}{2}(log{a} + log{b})

若a2 + b2 = 14ab, 试证 log{\frac{a+b}{4}} = \frac{1}{2}(log{a} + log{b})

3.

Given that 2^x = 9^y = 125^z = 120, prove that \frac{3}{x} + \frac{1}{2y} + \frac{1}{3z} =1

已知2^x = 9^y = 125^z = 120, 试证 \frac{3}{x} + \frac{1}{2y} + \frac{1}{3z} =1

4.

Given that a, b, c are positive and 3^a = 4^b = 6^c , prove that \frac{2}{c} = \frac{2}{a} + \frac{1}{b} .

已知 a, b, c 是正值且 3^a = 4^b = 6^c , 试证 \frac{2}{c} = \frac{2}{a} + \frac{1}{b} .