Question

"Свойства логарифмов" решить

Answer 1

$1)quad log_413cdot log_{13}16= frac{log_213}{log_24}cdot frac{log_216}{log_213} = frac{log_22^4}{log_22^2} =frac{4}{2}=2\\ili\\log_413cdot log_{13}16=log_413cdot frac{1}{log_{16}13}= frac{log_{4}13}{log_{4^2}13}= frac{log_413}{frac{1}{2}log_413} = frac{2cdot log_413}{log_413} =2\\2)quad frac{6^{log_{12}432}}{6^{log_{12}3}} =6^{log_{12}432-log_123}=6^{log_{12}frac{432}{3}}=6^{log_{12}144}=6^{log_{12}12^2}=\\=6^{2log_{12}12}=6^2=36$

$3)quad 75cdot log_{11}sqrt[3]{11}=75cdot log_{11}11^{frac{1}{3}}=75cdot frac{1}{3}log_{11}11=25$