Question

сравнить числа (1/5)^lg(1/7) и (1/7)^lg(1/5)

Answer 1

$\displaystyle(\frac{1}{5})^{\displaystyle lg(\frac{1}{7})}=(\frac{1}{7})^{\displaystyle lg(\frac{1}{5})}\\lg((\frac{1}{5})^{\displaystyle lg(\frac{1}{7})})=lg((\frac{1}{7})^{\displaystyle lg(\frac{1}{5})})\\lg(\frac{1}{5})lg(\frac{1}{7})=lg(\frac{1}{7})lg(\frac{1}{5})$