Convert natural exponent, $e^{c\cdot x}$, into the form $a^{x}$

Question

How does one convert a natural exponent written as $e^{c\cdot x}$ into the form $a^{x}$ ?

Answer 1

Since you can put $e^c=a$, you have that

$$e^{c \cdot x} = (e^c)^x=a^x$$

If you have that $a$ is some other number you can choose $c=\log a$ to get $e^c = a$