Question

How do you evaluate `e^(In8)`?

Answer 1

`e^ln(8) = 8`

Explanation:

Assuming the intended question is to evaluate `e^ln(8)`:

The base `b` logarithm is the inverse of an exponential function with base `b`. Specifically, it is the value to which `b` must be raised to obtain the argument of the function.

`log_b(x) = y iff x = b^y`

Note, then, that by definition: `a^(log_a(x)) = a^y = x`

(Note that it should make intuitive sense as to why `a^(log_a(x))=x`, as `log_a(x)` is the power to which we would need to raise `a` to obtain `x`, and we are raising `a` to that power)

The natural logarithm, or `ln`, is the logarithm with the base `e`. With that, we have

`e^ln(8) = e^(log_e(8)) = 8`