Log and Ln rules

$ \begin{array}{c@{\qquad}c} \textbf{Logarithm Rules (base 10)} & \textbf{Natural Log Rules} \\[8pt] \log(xy) = \log(x) + \log(y) & \ln(xy) = \ln(x) + \ln(y) \\[6pt] \log\!\left(\frac{x}{y}\right) = \log(x) - \log(y) & \ln\!\left(\frac{x}{y}\right) = \ln(x) - \ln(y) \\[6pt] \log(x^a) = a\log(x) & \ln(x^a) = a\ln(x) \\[6pt] \log(10^x) = x & \ln(e^x) = x \\[6pt] 10^{\log(x)} = x & e^{\ln(x)} = x \end{array} $