Question

How do you write `ln 8 = 2.08` in exponential form?

Answer 1

`8 = e^2.08`

Explanation:

Going from logarithmic to exponential form involves putting both sides of the equation to the power of an exponential function.

Basically, that means doing the inverse operation to both sides. Here, we have the natural log function; the inverse of that is the exponential function `e^x`. So, we put both sides to the power of `e`:

`e^(ln8) = e^2.08`

One of the rules of `e` is that `e^lnx = x`. Using this info, we can say that `e^ln8 = 8`. Applying this to the problem,

`8 = e^2.08`

Since we have an exponent, and not a logarithm, in our equation now, we've done it - gone from logarithmic to exponential form.