Exponential and Logarithmic Properties Retake

$$\log\frac{x}{y^6} = \log x - 6\log y$$ (Quotient Rule and Power Rule)

$$\log(ab)^2 = 2\log a + 2\log b$$ (Power Rule and Product Rule)

It implies that $$x^3 = 1000$$ , hence $$x = 10$$ .

$$\log_2 32 = 5$$ because $$2^5 = 32$$ .

$$\log_b a = \frac{\log_k a}{\log_k b}$$ for any base k.

$$\log_b(mn) = \log_b m + \log_b n$$ .

$$\log_b\left(\frac{m}{n}\right) = \log_b m - \log_b n$$ .

$$\log_b(m^p) = p \log_b m$$ .

$$b^c = a$$ .

$$\log_2 8 = 3$$ because $$2^3 = 8$$ .