Question

Помогите решить логорифм 98 баллов

Answer 1

$log_{15}^29+log_{15}5cdot log_{15}45=Big (frac{log_39}{log_315}Big )^2+frac{log_35}{log_315}cdot frac{log_345}{lig_315}=\\=Big (frac{log_33^2}{log_3(3cdot 5)}Big )^2+frac{log_35}{log_3(3cdot 5)}cdot frac{log_3(3^2cdot 5)}{log_3(3cdot 5)}=\\=Big (frac{2}{log_33+log_35}Big )^2+frac{log_35cdot (log_33^2+log_35)}{(log_33+log_35)^2}=; Big [; a=log_35approx 1,464977; Big ]; =\\=frac{4}{(1+a)^2}+frac{acdot (2+a)}{(1+a^2)}=frac{4+2+a^2}{(1+a)^2}=frac{(a+1)^2+3}{(a+1)^2}=frac{(a+1)^2}{(a+1)^2}+frac{3}{(a+1)^2}=$

$=1+frac{3}{(a+1)^2}approx 1+frac{3}{(1+1,465)^2}=1+0,494=1,494$