The exponential function of general base $\mathbb R\to\mathbb R,~x\to a^x$, is invertible for all positive bases $a > 0$. Its inverse function is continuous, strictly monotonically increasing and called the logarithm to the base $a$ \[\log_a:\mathbb R_{+}^*\to\mathbb R.\]
Furthermore, $\log_a$ (the logarithm to the base $a$) can be calculated using $\ln$ (i.e. the natural logarithm) by the formula $$\log_a(x)=\frac{\ln (x)}{\ln(a)},$$ for all $x\in\mathbb R_{+}^*.$
Proofs: 1
