# How do you calculate log_6 73 with a calculator?

Aug 31, 2016

$x = 2.395$

#### Explanation:

Log form and index form are interchangeable.

${\log}_{a} b = c \Leftrightarrow {a}^{c} = b$

Let ${\log}_{6} 73 = x \Leftrightarrow {6}^{x} = 73$

The variable is in the index, so we need logs.

$\log {6}^{x} = \log 73$

$x \log 6 = \log 73$

$x = \log \frac{73}{\log} 6$

$x = 2.395$