Question

Which exponential equation is equivalent to the logarithmic equation below? c = ln 2

Answer 1

$\text{A logarithmic lemma: } \\ \text{It follows that: } \log_a a = 1$
$\text{Following this property, we can see that: } a^{\log_{a} a} = a$
$\text{Furthermore, we can create more general properties: } a^{\log_a b} = b$

$c = \log_e 2 \Rightarrow e^{c} = e^{\log_e 2} \\ \text{Using our third property, we see that: } e^{c} = 2$
$\text{And finally, this works for any } \log_{a} b \left\{a > 0, b \in \mathbb{R}\right\}$