Methods for solving logarithmic inequalities

$\log_a f>\log_a g$

On $(0,+\infty)$ for $a>1$ the logarithm increases: $\log_a f>\log_a g\ \Leftrightarrow\ f>g$ (with $f,g>0$ ). For $0<a<1$ the inequality flips: $\log_a f>\log_a g\ \Leftrightarrow\ f<g$ . Then intersect with the domain: $f>0$ , $g>0$ .

Like $a^x$ , the branch $0<a<1$ reverses the inequality

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