Logarithms

Positive real numbers : x, y, a, c, k

Natural number : n

1 . \log_{a} 1 = 0

2 . \log_{a} a = 1

3 . \log_{a} 0 = - \infty if a > 1 and + \infty if a \lt 1

4 . \log_{a} (x y) = \log_{a} x + \log_{a} y

5 . \log_{a} (\frac{x}{y}) = \log_{a} x - \log_{a} y

6 . \log_{a} (x^{n}) = n \log_{a} x

7 . \log_{a} \sqrt[n]{x} = \frac{1}{n} \log_{a} x

8 . \log_{a} x = \frac{\log_{c} x}{\log_{c} a} = \log_{c} x - \log_{a} c, c > 0, c \neq 1

9 . \log_{a} c = \frac{1}{\log_{c} a}

10 . x = a^{\log_{a} x}

11 . \log_{10} x = \log x

12 . \log_{e} x = \ln x

13 . \log_{x} = \frac{1}{\ln 10} 1 n x = 0.434294 1 n x

14 . \ln x = \frac{1}{\log_{e}} \log x = 2.302585 \log x

Logarithms – Algebra Formulas