Question

Логарифмы, очень нужна помощь!

Answer 1

 

$169. \ log_a(ab^3) = log_a(a)+log_a(b^3) =\\ 1 + 3log_a(b) = 1+3\frac{1}{log_b(a)} = 1+3*7 = 22\\\\ 170. log_a(\frac{a}{b^3}) = log_a(a)-log_a(b^3) = 1-3log_a(b) = 1-15 = -14\\\\ 171. log_a(a^2b^3) = log_a(a^2)+log_a(b^3) =\\ 2log_a(a)+3log_a(b) = 2 - 6 = -4\\\\ 172. (3^{log_2(3)})^{log_3(2)} = 3^{log_2(3)*log_3(2)} =3^{log_2(3)\frac{1}{log_2(3)}} = 3^1 = 3$