Question

помогите мне пж срочно

Answer 1

$1)quad frac{7^{log_72}}{log_5frac{1}{25}} = frac{2}{log_55^{-2}} = frac{2}{-2}=-1 \\2)quad 12^{3-log_{12}2}=12^3cdot 12^{-log_{12}2}=12^3cdot 12^{log_{12}2^{-1}}=12^3cdot 2^{-1}=\\=frac{12^3}{2}=6cdot 12^2=864\\3)quad log_{sqrt2}(4cosfrac{pi}{8})+log_{sqrt2}(sinfrac{pi}{8})=log_{sqrt2}(4cosfrac{pi}{8}cdot sinfrac{pi}{8})=\\=log_sqrt2}(2sinfrac{pi}{4})=log_{2^{1/2}}(2cdot frac{sqrt2}{2})=2cdot log_2sqrt2=2cdot log_22^{1/2}=\\=2cdot frac{1}{2}=1$