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\}`