log10(x^3) + log10(y^2) = 11 log10(x^2) + log10(y^3) = 3 求解方程组.

问题描述:

log10(x^3) + log10(y^2) = 11 log10(x^2) + log10(y^3) = 3 求解方程组.

log10(x^3) + log10(y^2) = 11,可得:x^3y^2=10^11 log10(x^2) + log10(y^3) = 3 ,可得:x^2y^3=10^3 则有:x^3y^2/(x^2y^3)=10^11/10^3,可得:x/y=10^8,x=10^8y 将x=10^8y代入x^3y^2=10^11,则有:(10^8y)^3y^2=10^11 10^24y^5=10^11 y^5=10^(-13) y=10^(-13/5) 所以:x=10^8y=10^8*10^(-13/5)=10^(27/5) 所以方程组的解为:x=10^(27/5),y=10^(-13/5) 其中对数的运算公式必须清楚:loga(M)+loga(N)=loga(MN)