Let $a\ge 3,b\ge3,c\ge3$. Prove that: $$\log_{2b+c}a+\log_{2c+a}b+\log_{2a+b}c\ge\frac{3}{2}$$
I don't know what to do. Rewrite to $\ln(x)$ or $e^x$ But it's not work
Let $a\ge 3,b\ge3,c\ge3$. Prove that: $$\log_{2b+c}a+\log_{2c+a}b+\log_{2a+b}c\ge\frac{3}{2}$$
I don't know what to do. Rewrite to $\ln(x)$ or $e^x$ But it's not work