F.4maths 關於log~~~~~~~~~~~

2010-08-19 6:21 am
1)
Simplify logx^4+log8y^3-log4x^4y^2 / log4y^2
where x>0, y>0 and y is not equal to 1/2

2)
Solve logx+log(2x-7) / log(x-2) = 2

回答 (1)

2010-08-19 6:31 am
✔ 最佳答案
1)(logx^4 + log8y^3 - log4x^4 y^2) / log4y^2= {log [(x^4)(8y^3) / (4x^4 y^2)]} / log4y^2= [log (2y)] / log(2y)^2= (log 2y) / (2log 2y)= 1/22)[logx+log(2x-7)] / log(x-2) = 2 logx+log(2x-7) = 2 log(x - 2)log x(2x - 7) = log (x - 2)^2x(2x - 7) = (x - 2)^22x^2 - 7x = x^2 - 4x + 4x^2 - 3x - 4 = 0(x - 4)(x + 1) = 0x = 4 or x = - 1 (rejected)


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