Question

Найдите значение выражения $\frac{log_{3}5 }{log_{3}7 }+log_{7}0.2$

Answer 1

$\dfrac{\log_{3}5 }{\log_{3}7 }+\log_{7}0,2=\log_{7}5+\log_{7}0,2=\log_{7}(5\cdot 0,2)=\log_{7}1=\boxed0$

Answer 2

log(a) b = log(c) b / log(c) a

log(a) b + log(a) c = log(a) bc

log(3)5 / log(3) 7 = log(7) 5

log(7) 5 + log(7) 0.2 = log(7) 5*0,2 = log(7) 1 = 0