Question

Помогите решить логорифм 98 баллов

Answer 1

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

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