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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}= \
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= frac{2log_{3}5+log_{3}20}{log_{3}20-log_{3}5}= frac{2b+a}{a-b}= frac{a+2b}{a-b}](https://tex.z-dn.net/?f=log_%7B4%7D500%3D+frac%7Blog_%7B3%7D500%7D%7Blog_%7B3%7D4%7D%3D+frac%7Blog_%7B3%7D%285%5E2%2A20%29%7D%7Blog_%7B3%7D%2820%3A5%29%7D%3D+frac%7Blog_%7B3%7D5%5E2%2Blog_%7B3%7D20%7D%7Blog_%7B3%7D20-log_%7B3%7D5%7D%3D+%5C+%0A+%5C+%0A%3D+frac%7B2log_%7B3%7D5%2Blog_%7B3%7D20%7D%7Blog_%7B3%7D20-log_%7B3%7D5%7D%3D+frac%7B2b%2Ba%7D%7Ba-b%7D%3D+frac%7Ba%2B2b%7D%7Ba-b%7D++++++ "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}= \
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= 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](https://tex.z-dn.net/?f=log_%7B9%7D%28-2x-2%29+leq+-+frac%7B1%7D%7B2%7D+%5C+%0A+%5C+%0A-2x-2+textgreater++0+%5C+%0A-2x+textgreater++2+%5C+%0Ax+textless++-1+ "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}](https://tex.z-dn.net/?f=-2x-2+leq+9%5E%7B-+frac%7B1%7D%7B2%7D+%7D+%5C+%0A-2x-2+leq+%283%5E2%29%5E%7B-+frac%7B1%7D%7B2%7D+%7D+%5C+%0A-2x-2+leq+3%5E%7B-1%7D+%5C+%0A-2x+leq++frac%7B1%7D%7B3%7D%2B2+%5C+%0A-2x+leq+2+frac%7B1%7D%7B3%7D+%5C+%0A-2x+leq++frac%7B7%7D%7B3%7D+%5C+%0Ax+geq+-+frac%7B7%7D%7B6%7D++++ "-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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x∈[-7/6; -1)
8.
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------- -7/6 -------- -1 --------------
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x∈[-7/6; -1)
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