Logarithmic equations

Logarithmic to exponential form: $\log_b(x) = y$

$$b^y = x$$

Product property of logarithms: $\log_b(u \cdot v)$

$$\log_b(u) + \log_b(v)$$

Quotient property of logarithms: $\log_b\left(\frac{u}{v}\right)$

$$\log_b(u) - \log_b(v)$$

Power property of logarithms: $\log_b(u^p)$

$$p \cdot \log_b(u)$$

One-to-one property: if $\log_b(u) = \log_b(v)$

$$u = v$$

Change-of-base formula for $\log_b(a)$

$$\frac{\log_c(a)}{\log_c(b)}$$

Domain check for extraneous solutions in logarithmic equations

$\text{Argument} > 0$ for all logarithmic terms