# How do you calculate log_4 78 with a calculator?

Aug 6, 2016

$x = 3.1427$

#### Explanation:

Some calculators can calculate logs with bases other than base 10.
But for all calculators, follow this method:

${\log}_{4} 78 = x$

Write in index from:

${4}^{x} = 78 \text{ the variable is in the index - use logs}$

$x {\log}_{10} 4 = {\log}_{10} 78$

$x = \frac{{\log}_{10} 78}{{\log}_{10} 4}$

$x = 3.1427$

This can also be obtained directly using "The change of base rule"