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。
Answer:
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。
Answer:
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。
Answer:
If x=
*** QuickLaTeX cannot compile formula: \log_3{{\frac{16}{9}} *** Error message: Missing } inserted. leading text: $\log_3{{\frac{16}{9}}$
, y= and z= , find the values of
若 x=
*** QuickLaTeX cannot compile formula: \log_3{{\frac{16}{9}} *** Error message: Missing } inserted. leading text: $\log_3{{\frac{16}{9}}$
, y= 和 z= ,求值:
(a) + – z
(b) 2x + y + 2z
Answer:
If a=2 and b=2, find the value of 2a + b
若 a=2 及 b=2 , 求2a + b 的值。
Answer:
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.