The inverse function to exponentiation. If $b^y = x$, then $\log_b(x) = y$.

The logarithm with base e, denoted as $\ln(x)$.

The mathematical constant e, approximately equal to 2.71828.

Identify products within the logarithm, then split the log into a sum of logs: $\log_b(xy) = \log_b(x) + \log_b(y)$.

Identify exponents within the logarithm, then bring the exponent down as a multiplier: $\log_b(x^n) = n\log_b(x)$.

Use the change of base formula: $\log_b(x) = \frac{\log_{10}(x)}{\log_{10}(b)}$.

Apply properties to isolate the variable. Rewrite in exponential form if necessary.

$\log_b(xy) = \log_b(x) + \log_b(y)$

$\log_b(x^n) = n\log_b(x)$

$\log_b(x) = \frac{\log_a(x)}{\log_a(b)}$

$\ln(x) = \log_e(x)$