Logarithmic2

lena

2009-11-24 5:05 am

Please write the step clearly,and state the property you have been used

1. log base 25 9 × log base 27 5

=log base 5 9/log base 5 25 ×log base 3 5/log base 3 27

=???

2.log base 8 ^3√49/ log base 32 7

3.log base 25 (2x)-log base 5 8=0

4.2log base 4 (xy)+ log base 4 x^5/ 3 log base 4 x^4 - 4 log base 4√x/y

回答 (1)

用戶9112

2009-11-24 6:03 am

✔ 最佳答案

(1) [log(25) 9][log(27) 5]
= (log9/log25)(log5/log27)
= [(2log3)/(2log5)][log5/3log3]
= 1/3
(2) [log(8^3)√49] / [log(32) 7]
= [log(√49)/log(8^3)] / (log7/log32)
= [(log7)/(3log8)] * (5log2/log7)
= [(log7)/(9log2)] * (5log2/log7)
= 5/9
(3) [log(25) 2x] - [log(5) 8] = 0
log(2x) / log(25) = log8 / log5
log(2x) / (2log5) = log8 / log5
log(2x) = 2log8
log(2x) = log64
2x = 64
x = 32
(4) {[2log(4) xy] + [log(4) x^5]} / {[3log(4) x^3] - [4log(4)(√(x/y)]}
= {[log(4) x^2y^2] + [log(4) x^5]} / {[log(4) x^9] - [log(4) (x^2/y^2)]}
= {log(4) (x^2y^2)(x^5)} / {log(4) [(x^9)/(x^2/y^2)]}
= {log(4) (x^7y^2)} / {log(4) [(x^7y^2)]}
= 1

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