F.4 Maths logarithm

yuet

2009-12-05 5:23 pm

Find the value of 1/3 log2 27 + log2 12- 2 log2 3/4
without using a calculator
* the log2 means base on 2
find the value of (log(a) ∛216+1/4 log(a) 36)/(log(a) (1/9)-2log(a) 2) without using a calculator
* the log(a) is based on a

更新1:

Slove the equation [ log3 (4x-3)]^2 - 3 log3 (4x-3) -4=0 * the log3 is means based on 3

回答 (1)

用戶9112

2009-12-05 5:50 pm

✔ 最佳答案

(1/3)log_2 27 + log_2 12 - 2log_2(3/4)
= log_2 [27^(1/3) * 12 / (3/4)^2]
= log_2 [3 * 12 * 16/9]
= log_2 64
= log64/log2
= log2^6 / log2
= 6log2 / log2
= 6
[log_a (216)^(1/3) + (1/4) log_a 36] /[log_a (1/9) - 2 log_a 2]
= [log_a 6 + log_a (36)^(/14)] / [log_a (1/9) - log_a 4]
= [log_a 6(6)^(1/2)] / [log_a (1/9)/4]
= log_a 6^(3/2) / log_a (1/6^2)
= (3/2)log_a 6 / -2 log_a 6
= (3/2) / (-2)
= -3/4
[log_3 (4x - 3)]^2 - 3log_3 (4x-3) - 4 = 0
Let log_3 (4x - 3) = u
u^2 - 3u - 4 = 0
(u - 4)(u + 1) = 0
u = 4 or u = -1
log_3(4x - 3) = 4 or log_3(4x - 3) = -1
4x - 3 = 3^4 or 4x - 3 = 3^(-1)
4x - 3 = 81 or 4x - 3 = 1/3
4x = 84 or 4x = 10/3
x = 21 or x = 5/6

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