# Exponential function in terms of logarithms

1. Jul 16, 2007

### dimensionless

1. The problem statement, all variables and given/known data
Express $$b^{x}$$ as a function of logarithms.

2. Relevant equations
There are a couple of equations in the attempted solution. I can't say if they are actually relevant

3. The attempt at a solution

I've investigated the property
$$y = log_{b}(b^{y}),$$
and also
$$log_{b}(y) = \frac{log_{k}(y)}{log_{k}(b)}$$

This hasn't help me any.

2. Jul 16, 2007

### dimensionless

I got it. It's

$$b^{x} = e^{x ln(b)} = b + \frac{x ln(b)}{1!}+ \frac{(x ln(b))^{2}}{2!}+ \frac{(x ln(b))^{3}}{3!}+ \frac{(x ln(b))^{4}}{4!}+...$$

Last edited: Jul 16, 2007
3. Jul 17, 2007

### GoldPheonix

Never mind, my mistake.