Question

помогите с логарифмами, прошу

Answer 1

Ответ:

29) 49

30) 34

31) 14

32) -32

33) -35

Объяснение:

$a) log_{b}(a) = \frac{2}{15} \\\\log_{a}(a^4b^6) = log_{a}(a^4) + log_{a}(b^6) = 4 +\frac{1}{\frac{1}{6} log_{b}a} = 4 + \frac{6}{\frac{2}{15} } = 4 + 45 = 49$

$b) log_{b}(a) = \frac{2}{11} \\\\log_{a}(ab^6) = log_{a}(a) + log_{a}b^6 = 1 + \frac{6}{log_{b}(a)} = 1 + \frac{6}{\frac{2}{11} } = 1 +33 = 34$

$c) log_{a}(b) = -2\\\\log_{a}(\frac{a^6}{b^4} ) = log_{a}(a^6) - log_{a}(b^4) = 6 - 4 log_{a}(b) = 6 - 4*(-2) = 14$

$d) log_{a}(b) = 7;\\\\log_{a}(\frac{a^3}{b^5} ) = log_{a}(a^3) - log_{a}(b^5) = 3 - 5log_{a}(b) = 3 - 5*7 = -32$

$e) log_{a}(b) = -10; \\\\log_{a}(a^5b^4) = log_{a}(a^5) + log_{a}(b^4) = 5 + 4log_{a}(b) = 5 + 4*(-10) = -35$