Please help me to solve Maths!

2010-03-06 6:14 am

Please solve the following logarithmic equations:

1) logx3-log16x=-2

2) 1+log34X=log3(2x+5)

3) log4(5x-3)=log4(3x+1)-1/2

更新1:

1 = log 4 to base 4 (-1/2) = (-1/2) log 4 to base 4 = log 4^(-1/2) = log 2^(-1) to base 4 唔係太明白點解變成咁,可唔可以再詳細d??? thx

更新2:

真想想知解, 請大師指點, 謝謝.

回答 (1)

用戶10012

2010-03-06 4:02 pm

✔ 最佳答案

1.
log x^3 - log 16x = - 2 = log 10^(-2)
log (x^3/16x) = log (1/100)
x^3/16x = 1/100
x^2 = 16/100
x = 4/10 = 2/5.
2.
1 = log 3 to base 3.
the equation becomes
log 3 + log 4x = log (2x + 5) to base 3
log 12x = log (2x + 5)
12x = 2x + 5
10x = 5
x = 1/2.
3.
1 = log 4 to base 4
(-1/2) = (-1/2) log 4 to base 4 = log 4^(-1/2) = log 2^(-1) to base 4
so the equation becomes
log (5x - 3) = log (3x + 1) + log 2^(-1) to base 4
log (5x - 3) = log [(3x + 1)/2]
5x - 3 = (3x + 1)/2
10x - 6 = 3x + 1
7x = 7
x = 1.

2010-03-06 08:04:21 補充：
For Q3, log 2^(-1) = log (1/2), please note.

👍 0 👎 0