ɑ=log3(6)=log3(3×2)=log3(3)+log3(2)=1+log3(2);
b=log5(10)=log5(5×2)=log5(5)+log5(2)=1+log5(2);
c=log7(14)=log7(7×2)=log7(7)+log7(2)=1+log7(2);
∵函数y=logx(2)是减函数,
∴log3(2) > log5(2) log7(2)
∴ 1+log3(2) > 1+log5(2) > 1+log7(2)
即a>b>c
ɑ=log3(6)=log3(3×2)=log3(3)+log3(2)=1+log3(2);
b=log5(10)=log5(5×2)=log5(5)+log5(2)=1+log5(2);
c=log7(14)=log7(7×2)=log7(7)+log7(2)=1+log7(2);
∵函数y=logx(2)是减函数,
∴log3(2) > log5(2) log7(2)
∴ 1+log3(2) > 1+log5(2) > 1+log7(2)
即a>b>c