Question

известно что lg3=m lg5=n найдите log 45 4

Answer 1

$lg3=m; ,; ; lg5=n\\log_{45}4= frac{lg4}{lg45} = frac{lg2^2}{lg(5cdot 9)} = frac{2lg2}{lg5+lg3^2} = frac{2cdot lg2}{n+2lg3} = frac{2cdot lg(frac{10}{5})}{n+2m} =\\= frac{2cdot (lg10-lg5)}{n+2m} = frac{2(cdot (1-n)}{n+2m}$