Question

10 класс ,логарифмы,вычислите

Answer 1

a) $log_2{16}+log_{1/3}{9}=log_2{2^4}+log_{1/3}{(1/3)^{-2}}=4-2=2$
б) $5^{log_5{10}-1}=frac{5^{log_5{10}}}{5}=frac{10}{5}=2$
в) $log_69+2log_62=log_69+log_62^2=log_69+log64=log_6{9cdot4}=log_636=log_6{6^2}=2$

Answer 2

$log_{2} 16 + log_{ frac{1}{3}} 9 = 4 + frac{log_{3}9}{log_{3}frac{1}{3}} = 4 + frac{2}{-1} = 4-2=2 \ 5^{log_{5} 10 - 1} =5^{log_{5} 10} * 5^{ - 1} = 10 * frac{1}{5} = 2 \ log_{6} 9 + 2log_{6} 2 =log_{6} 9 + log_{6} 2^{2} =log_{6} 9 + log_{6} 4 =log_{6} (9*4)= \ =log_{6}36 = 2$