math Log數~ 急

[匿名]

2009-09-19 3:14 am

1.solve x in term of y in each of the eq.~
logx + log(1+y)^2 = log 9y/x

2.
solve the eq. :3(5^x+3)=4(72^x-1) , ans:::correct to 2 decimal places.

回答 (2)

用戶2053

2009-09-19 3:50 am

✔ 最佳答案

1)logx + log(1+y)^2 = log 9y/x

log [x(1+y)^2] = log 9y/x.............(logM + logN = logMN)

x(1+y)^2 = 9y/x

x^2 = 9y / (1+y)^2

x = (+ or - ) [3y^(1/2)] / (1+y)

2) 3(5^x+3)=4(72^x-1)

(3*5^3) (5^x) = (4/72) (72^x)

6750 = (72^x) / (5^x)

6750 = (72/5)^x

log 6750 = log (72/5)^x

log 6750 = x log (72/5)

x = (log 6750) / log (72/5)

x = 3.305790544 = 3.31 (correct to 2 decimal places.)

2009-09-18 19:51:45 補充：
For Q1 , - [3y^(1/2)] / (1+y) is rejected since x cannot be negative for log x.

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用戶9112

2009-09-19 3:51 am

x,y > 0

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