Question

Логарифмы, помогите решить

Answer 1

$\frac{log_2^23}{log_212}-\frac{log_248\cdot log_{12}2}{log_{48}2}=$

$\frac{log_2^23}{log_212}-\frac{log_248\cdot \frac{1}{log_212} }{ \frac{1}{log_248} }=$

$\frac{log_2^23}{log_212}-\frac{log_248\cdot log_248}{log_212}=$

$\frac{log_2^23-log_2^248}{log_212}=$

$\frac{(log_23-log_248) \cdot (log_23+log_248)}{log_212}=$

$\frac{log_2 \frac{3}{48}\cdot log_2(3 \cdot 48)}{log_212}=$

$\frac{log_2 \frac{1}{16}\cdot log_2144}{log_212}=$

$\frac{log_2 16^{-1}\cdot log_212^2}{log_212}=$

$\frac{-log_2 16\cdot 2log_212}{log_212}=$

$-2log_2 2^4=-8log_22=-8$