若函數(shù)f(x)=logaX(a>0且a≠1)滿足f(9)=2,f的-1次方(log9(2))之值是_____
熱心網(wǎng)友
f(x)=loga(x), == f^-1(x)=a^x又f(9)=loga(9)=2loga(3)=2, == loga(3)=1,== a=3所以：f^-1[log9(2)]=3^[log9(2)]={9^[log9(2)]}^(1/2)=2^(1/2)=√2
若函數(shù)f(x)=logaX(a>0且a≠1)滿足f(9)=2,f的-1次方(log9(2))之值是_____
f(x)=loga(x), == f^-1(x)=a^x又f(9)=loga(9)=2loga(3)=2, == loga(3)=1,== a=3所以：f^-1[log9(2)]=3^[log9(2)]={9^[log9(2)]}^(1/2)=2^(1/2)=√2