\flushbottom
\subsubsection*{Index identities}
\begin{align*}
- b^{m+n} &= b^m \cdot b^n \\
- (b^m)^n &= b^{m \cdot n} \\
- (b \cdot c)^n &= b^n \cdot c^n \\
- {a^m \div a^n} &= {a^{m-n}}
+ a^{x+y} &= a^x \cdot a^y \\
+ a^{x-y} &= a^x \div a^y \\
+ (a^x)^y &= a^{x \cdot y} \\
+ (a \cdot b)^x &= a^x \cdot b^x
\end{align*}
}
\begin{align*}
\log_b (xy) &= \log_b x + \log_b y \\
\log_b\left(\frac{x}{y}\right) &= \log_b(x) - \log_b(y) \\
- \log_b x^n &= n \log_b x \\
- \log_b y^{x^n} &= x^n \log_b y
+ \log_b y^{x^n} &= x^n \log_b y \\
+ \log_b x^n &= n \log_b x
\end{align*}
}