已知3的2x次方=4的3x次方=12的6次方,求3/x+2/y的值令3^2x=4^3y=12^6=K则log3(k)=2X,log4(k)=3y,log12(k)=6 (1)把(1)变形logk(3)=1/2X,logk(4)=1/3Y,logk(12)=1/6logk(3)+logk(4)=1/2x+1/3y即logk(12)=1/2x+1/3y=1/6 分子分母通分即(3y+2
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 13:45:19
![已知3的2x次方=4的3x次方=12的6次方,求3/x+2/y的值令3^2x=4^3y=12^6=K则log3(k)=2X,log4(k)=3y,log12(k)=6 (1)把(1)变形logk(3)=1/2X,logk(4)=1/3Y,logk(12)=1/6logk(3)+logk(4)=1/2x+1/3y即logk(12)=1/2x+1/3y=1/6 分子分母通分即(3y+2](/uploads/image/z/3736166-14-6.jpg?t=%E5%B7%B2%E7%9F%A53%E7%9A%842x%E6%AC%A1%E6%96%B9%3D4%E7%9A%843x%E6%AC%A1%E6%96%B9%3D12%E7%9A%846%E6%AC%A1%E6%96%B9%2C%E6%B1%823%2Fx%2B2%2Fy%E7%9A%84%E5%80%BC%E4%BB%A43%5E2x%3D4%5E3y%3D12%5E6%3DK%E5%88%99log3%28k%29%3D2X%2Clog4%28k%29%3D3y%2Clog12%28k%29%3D6+%281%29%E6%8A%8A%EF%BC%881%EF%BC%89%E5%8F%98%E5%BD%A2logk%283%29%3D1%2F2X%2Clogk%284%29%3D1%2F3Y%2Clogk%2812%29%3D1%2F6logk%283%29%2Blogk%284%29%3D1%2F2x%2B1%2F3y%E5%8D%B3logk%2812%29%3D1%2F2x%2B1%2F3y%3D1%2F6+%E5%88%86%E5%AD%90%E5%88%86%E6%AF%8D%E9%80%9A%E5%88%86%E5%8D%B3%283y%2B2)
已知3的2x次方=4的3x次方=12的6次方,求3/x+2/y的值令3^2x=4^3y=12^6=K则log3(k)=2X,log4(k)=3y,log12(k)=6 (1)把(1)变形logk(3)=1/2X,logk(4)=1/3Y,logk(12)=1/6logk(3)+logk(4)=1/2x+1/3y即logk(12)=1/2x+1/3y=1/6 分子分母通分即(3y+2
已知3的2x次方=4的3x次方=12的6次方,求3/x+2/y的值
令3^2x=4^3y=12^6=K
则log3(k)=2X,log4(k)=3y,log12(k)=6 (1)
把(1)变形
logk(3)=1/2X,logk(4)=1/3Y,logk(12)=1/6
logk(3)+logk(4)=1/2x+1/3y
即logk(12)=1/2x+1/3y=1/6 分子分母通分即(3y+2x)/6xy
又因为:3/x+2/y=(3y+2x)/xy(分子分母通分)
两式相差了1/6
即(3y+2x)/6xy*6就等于要求的式子,即1/6*6=1
为何log12(k)=6可以转化为logk(12)=1/6
已知3的2x次方=4的3x次方=12的6次方,求3/x+2/y的值令3^2x=4^3y=12^6=K则log3(k)=2X,log4(k)=3y,log12(k)=6 (1)把(1)变形logk(3)=1/2X,logk(4)=1/3Y,logk(12)=1/6logk(3)+logk(4)=1/2x+1/3y即logk(12)=1/2x+1/3y=1/6 分子分母通分即(3y+2
log12(k)=6,【利用换底公式:loga b=logc b/(logc a)】
logk(k)/[logk(12)]=6
1/[logk(12)]=6
logk(12)=1/6