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17.3 Change of Base of Logarithms 对数的换底公式

1.

Given log 3 = m, log 2 = n, prove that = .

2.

If log = a, state log x in terms of a.

1.5a
3.

Given that log 3 = a and log 7 = b. State log 56 in terms of a and b. 4.

Show that log xy = 2log x + 2log y. Hence or otherwise, find the values of x and y that satisfies the equation log xy = 10 and = .

16, 64
5.

If x=

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, y= and z= , find the values of

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, y= 和 z= ，求值：

(a) + – z

(b) 2x + y + 2z

16, 64
6.

If a=2 and b=2 , find the value of 2a + b 9

7.

8.

If , are the roots of 3(log x)2 – 2log x + 1 = 0, form a quadratic equation which roots are log , log . , 是方程式 3(log x)2 – 2log x + 1 = 0 的根, 试作一个一元二次方程式，使它的两个根是 log , log .

3x + 5x + 3 = 0 