# Question #e45e9

Jun 18, 2017

The limit equals approximately $0.85$

#### Explanation:

Here's a table of values

As you can see, the closer the number gets to $0$, the less the y-variable, that's to say the output, varies.

If we check our work using l'hospitals rule, we get:

$L = {\lim}_{x \to 0} \frac{{7}^{x} \ln \left(7\right) - {3}^{x} \ln \left(3\right)}{1}$

$L = \ln \left(7\right) - \ln \left(3\right)$

$L \approx 0.85$

So our estimation using the table was quite precise.

Hopefully this helps!