# How do you calculate Log_4 14?

Sep 30, 2016

I supposed that you can use a calculator.

#### Explanation:

One way involves the use of a scientific calculator that allows you to evaluat a natural logarithm indicated as $\ln$.
You can change base of your original log using a well known relationship where you get a fraction of two logs in the new base and as arguments the old argument and the old base:
${\log}_{4} \left(14\right) = \ln \frac{14}{\ln} \left(4\right) = 1.90367$

You can test this result considering that (using the definition of log):

${4}^{1.90367} = 13.9998 \approx 14$