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\[\frac{\log _8 x}{\log _8\left(\frac{x}{64}\right)} \geq \frac{2}{\log _8 x}+\frac{3}{\log _8^2 x-\log _8 x^2} .\]
\[\frac{\log _4\left(16 x^4\right)+11}{\log _4^2 x-9} \geq-1 .\]
\[\log _2\left(4 x^2-1\right)-\log _2 x \leq \log _2\left(5 x+\frac{9}{x}-11\right) .\]
\[\log _2^2\left(x^2-9\right)-9 \log _2\left(x^2-9\right)+20 \geq 0 .\]
\[\frac{8^{x+\frac{2}{3}}-9 \cdot 4^{x+\frac{1}{2}}+13 \cdot 2^x-13}{4^{x+\frac{1}{2}}-9 \cdot 2^x+4} \leq 2^{x+1}-\frac{1}{2^x-2}+\frac{3}{2^{x+1}-1} .\]
\[\frac{4^x-3 \cdot 2^{x+1}+4}{2^x-5}+\frac{3 \cdot 2^{x+1}-46}{2^x-8} \leq 2^x+5 .\]
