Question

Помогите с логарифмами, очень срочно

Answer 1

7.
$log_{4}500= frac{log_{3}500}{log_{3}4}= frac{log_{3}(5^2*20)}{log_{3}(20:5)}= frac{log_{3}5^2+log_{3}20}{log_{3}20-log_{3}5}= \ \ = frac{2log_{3}5+log_{3}20}{log_{3}20-log_{3}5}= frac{2b+a}{a-b}= frac{a+2b}{a-b}$

8.
$log_{9}(-2x-2) leq - frac{1}{2} \ \ -2x-2 textgreater 0 \ -2x textgreater 2 \ x textless -1$

$-2x-2 leq 9^{- frac{1}{2} } \ -2x-2 leq (3^2)^{- frac{1}{2} } \ -2x-2 leq 3^{-1} \ -2x leq frac{1}{3}+2 \ -2x leq 2 frac{1}{3} \ -2x leq frac{7}{3} \ x geq - frac{7}{6}$
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------- -7/6 -------- -1 --------------
                /////////////////////////////////
x∈[-7/6; -1)