Question

Помогите найти логарифм числа 81 по основанию 105

Answer 1

$x=log_{105}(81) = log_{105}(9^2) = log_{105}(3^4) = 4log_{105}3$
$a+b = log_{105}5 + log_{105}7 = log_{105}(5cdot7) =$
$= log_{105}(35) = log_{105}(frac{35cdot 3}{3}) =$
$= log_{105}(frac{105}{3}) = log_{105}(105) - log_{105}(3) =$
$= 1 - log_{105}(3)$.
Отсюда,
$log_{105}(3) = 1 - a - b$
$x = 4cdot (1 - a - b)$