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標題:
中四maths log問題;(20分)急;
發問:
1.若log x+log 2y=2,以x表y. 2.設log 2=a及log 3=b.以a及b表log開方45. 3.化簡log x(3次方)+log開方x除以2 log1除x.
1. log x + log 2y = 2 log (2xy) = 2 2xy = 10^2 = 100 xy = 50 y = 50/x 2. log√45 = log [45^(1/2)] = 1/2 log 45 = 1/2 log (3^2 * 10 / 2) = 1/2 [log 3^2 + log 10 - log 2] = 1/2 [2 log 3 + 1 - log 2] = 1/2 (2b + 1 - a) = -a/2 + b + 1/2 3. [log (x^3) + log√x] / [2 log(1/x)] = [log (x^3) + log (x^{1/2})] / [2 log (x^{-1})] = [3 log x + 1/2 log x] / [-2 log x] = (3 + 1/2) / (-2) = -7/4
其他解答:
中四maths log問題;(20分)急;
發問:
1.若log x+log 2y=2,以x表y. 2.設log 2=a及log 3=b.以a及b表log開方45. 3.化簡log x(3次方)+log開方x除以2 log1除x.
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最佳解答:1. log x + log 2y = 2 log (2xy) = 2 2xy = 10^2 = 100 xy = 50 y = 50/x 2. log√45 = log [45^(1/2)] = 1/2 log 45 = 1/2 log (3^2 * 10 / 2) = 1/2 [log 3^2 + log 10 - log 2] = 1/2 [2 log 3 + 1 - log 2] = 1/2 (2b + 1 - a) = -a/2 + b + 1/2 3. [log (x^3) + log√x] / [2 log(1/x)] = [log (x^3) + log (x^{1/2})] / [2 log (x^{-1})] = [3 log x + 1/2 log x] / [-2 log x] = (3 + 1/2) / (-2) = -7/4
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