已知:3的x次方＝5的y次方＝m,且1/x+1/y=2,则m等于几?还有一个,log(根2为底)(根号下6+4根2)-(根号下6-4根2)=多少
问题描述：
已知:3的x次方＝5的y次方＝m,且1/x+1/y=2,则m等于几?
还有一个,
log(根2为底)(根号下6+4根2)-(根号下6-4根2)=多少
答
x=log3(m) y=log5(m)
1/x+1/y=logm(3)+logm(5)=logm(15)=2
所以m=根下15
log(根2为底)(根号下6+4根2)-(根号下6-4根2)＝
logsqrt(2)【根下(根2+2)^2-根下(根2-2)^2]=log2[(根2+2)+(根2-2)]=log2(2根2）＝3
答
3的x次方＝5的y次方＝m,x=log(3为底)m,y=log(5为底)m且1/x+1/y=2,→1/log(3为底)m+1/log(5为底)m=2→log(m为底)3+log(m为底)5=2→log(m为底)(3*5)=2→m^2=15,∴m=√156+4√2=4+4√2+2=2^2+2*2√2+√2^2=(2+√2)^2∴(...