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中四log數問題 數學高手請進
http://x5a.xanga.com/1e6f607415c35259068249/b206272438.jpg http://xf8.xanga.com/90ef7a7475c35259068248/b206272437.jpg http://x58.xanga.com/439f767455c32259068247/b206272436.jpg http://xca.xanga.com/80ff464768333259068227/b206272421.jpg ans. 30]x/y+2/3 31]2x-1 37]1 39]沒有解 40]1/3 41]32 求過程
最佳解答:
30. 已知 log5_2=x，log5_3=y，以x和y表示 log27_72 Sol x=log2/log5 =>log2=xlog5 y=log3/log5 =>log3=ylog5 log27_72 =log72/log27 =(3log2+2log3)/(3log3) =(3x+2y)/3y 31已知 log25_10=x，試以x表示 log5_2 Sol x=log10/log25=log10/log(100/4)=1/(2－2log2) 2－2log2=1/x 2log2=2－1/x=(2x－1)/x 2log5=2－2log2=2－(2x－1)/(x)=1/x log5_2=log2/log5=2x－1 37 .[2log4(xy)+log4x^5]/[3log4x^3－4log(sqrt(x/y)] Sol x>0，y>0 [2log4(xy)+log4x^5]/[3log4x^3－4log(sqrt(x/y)] =[2log4+2logx+2logy+log4+5logx]/[3log4+9logx－2log(x/y)] =[2log4+2logx+2logy+log4+5logx]/[3log4+9logx－2logx+2logy] =[3log4+7logx+2logy]/[3log4+7logx+2logy] =1 39. log4(x+3)=log4(x－3)－2 Sol log4(x+3)=log[4(x－3)/100] 4(x+3)=4(x－3)/100 25(x+3)=x－3 25x+75=x－3 24x=－78 x=－78/24=－13/4(不合無解) 40 logx_9+log11_121=0 Sol logx_9+2=0 logx_9+logx_(x^2)=0 9x^2=1 x=1/3 or x=－1/3(不合) 41 log25_(2x)-log5_8=0 Sol log25_(2x)=log5_8 log(2x)/log25=log8/log5 log(2x)=2log8 2x=64 x=32
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中四log數問題 數學高手請進
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發問:http://x5a.xanga.com/1e6f607415c35259068249/b206272438.jpg http://xf8.xanga.com/90ef7a7475c35259068248/b206272437.jpg http://x58.xanga.com/439f767455c32259068247/b206272436.jpg http://xca.xanga.com/80ff464768333259068227/b206272421.jpg ans. 30]x/y+2/3 31]2x-1 37]1 39]沒有解 40]1/3 41]32 求過程
最佳解答:
30. 已知 log5_2=x，log5_3=y，以x和y表示 log27_72 Sol x=log2/log5 =>log2=xlog5 y=log3/log5 =>log3=ylog5 log27_72 =log72/log27 =(3log2+2log3)/(3log3) =(3x+2y)/3y 31已知 log25_10=x，試以x表示 log5_2 Sol x=log10/log25=log10/log(100/4)=1/(2－2log2) 2－2log2=1/x 2log2=2－1/x=(2x－1)/x 2log5=2－2log2=2－(2x－1)/(x)=1/x log5_2=log2/log5=2x－1 37 .[2log4(xy)+log4x^5]/[3log4x^3－4log(sqrt(x/y)] Sol x>0，y>0 [2log4(xy)+log4x^5]/[3log4x^3－4log(sqrt(x/y)] =[2log4+2logx+2logy+log4+5logx]/[3log4+9logx－2log(x/y)] =[2log4+2logx+2logy+log4+5logx]/[3log4+9logx－2logx+2logy] =[3log4+7logx+2logy]/[3log4+7logx+2logy] =1 39. log4(x+3)=log4(x－3)－2 Sol log4(x+3)=log[4(x－3)/100] 4(x+3)=4(x－3)/100 25(x+3)=x－3 25x+75=x－3 24x=－78 x=－78/24=－13/4(不合無解) 40 logx_9+log11_121=0 Sol logx_9+2=0 logx_9+logx_(x^2)=0 9x^2=1 x=1/3 or x=－1/3(不合) 41 log25_(2x)-log5_8=0 Sol log25_(2x)=log5_8 log(2x)/log25=log8/log5 log(2x)=2log8 2x=64 x=32
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