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Change of base formula
For $a>0$, $a\neq 1$, $b>0$, and any convenient base $c>0$, $c\neq 1$:
$$\log_a b=\frac{\log_c b}{\log_c a}$$
Common choices are $c=10$ (using $\log$) or $c=e$ (using $\ln$).
Feasible region
The set of all points that satisfy every inequality in a system (all constraints). Graphically, it is the overlap region, often a polygon.
Logarithm
For $a>0$, $a\neq 1$, and $x>0$, $\log_a x$ is the exponent $k$ such that $a^k=x$.
Non-Linear Inequality
An inequality where the expressions are not linear, for example involving $x^2$, $\sqrt{x}$, $e^x$, $\log x$, or $\frac{1}{x}$.
Non-linear inequality (in two variables)
An inequality involving $x$ and $y$ whose boundary is a non-linear curve (for example, a parabola, exponential curve, logarithmic curve, or rational curve). Its solution is a set of points (a shaded region) in the plane.
Non-strict inequality
An inequality using $\le$ or $\ge$, meaning the boundary is included in the solution set.
Power rule
$\log_a(x^n)=n\log_a x$ (for real $n$, as long as $x^n$ is defined and $x>0$).
Product rule
$\log_a(xy)=\log_a x+\log_a y$.
Quotient rule
$\log_a\left(\frac{x}{y}\right)=\log_a x-\log_a y$.
Strict inequality
An inequality using $<$ or $>$, meaning the boundary is not included in the solution set.