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

1.

Given log3 = m, log2 = n, prove that = .

已知 log3 = m, log2 = n, 试证 = .

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

若log = a, 用a 表示 logx。

Given that log3 = a and log7 = b. State log56 in terms of a and b.

已知log3 = a and log7 = b。 以 a 和 b 表示 log56。

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

试证 logxy = 2logx + 2logy. 据此或其他方法, 求满足方程式 logxy = 10 和 = 的 x 及 y 之值。

If x=

*** QuickLaTeX cannot compile formula:
\log_3{{\frac{16}{9}}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timeout after 10001 ms
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37

, y= and z= , find the values of

若 x=

*** QuickLaTeX cannot compile formula:
\log_3{{\frac{16}{9}}

*** Error message:
Cannot connect to QuickLaTeX server: cURL error 28: Connection timeout after 10001 ms
Please make sure your server/PHP settings allow HTTP requests to external resources ("allow_url_fopen", etc.)
These links might help in finding solution:
http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37

, y= 和 z= ，求值：

(a) + – z

(b) 2x + y + 2z

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

若 a=2 及 b=2 , 求2a + b 的值。

7.

试证 – = 1

If , are the roots of 3(logx)2 – 2logx + 1 = 0, form a quadratic equation which roots are log, log.

若 , 是方程式 3(logx)2 – 2logx + 1 = 0 的根, 试作一个一元二次方程式，使它的两个根是 log, log.