CHAPTER 13 KEY FORMULAS AND EQUATIONS

Exponential function	$y = b^{x}$ (13.1)
Logarithmic form	$x = \log_{b} y$ (13.2)
Logarithmic function	$y = \log_{b} x$ (13.3)
Laws of exponents	$b^{u} b^{v} = b^{u + v}$ (13.4) $\frac{b^{u}}{b^{v}} = b^{u - v}$ (13.5) ${(b^{u})}^{n} = b^{n u}$ (13.6)
Properties of logarithms	$\log_{b} x y = \log_{b} x + \log_{b} y$ (13.7) $\log_{b} (\frac{x}{y}) = \log_{b} x - \log_{b} y$ (13.8) $\log_{b} (x^{n}) = n \log_{b} x$ (13.9) $\log_{b} 1 = 0 \log_{b} b = 1$ (13.10) $\log_{b} (b^{x}) = x$ (13.11) $b^{\log_{b} x} = x$ (13.12)
Change-of-base-formula	$\log_{b} x = \frac{\log_{a} x}{\log_{a} b}$ (13.13)
Base e properties	$\ln (e^{x}) = x$ (13.14) $e^{\ln x} = x$ (13.15)

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Basic Technical Mathematics, 11th Edition by Allyn J. Washington, Richard Evans