# How do you calculate log_4 57 with a calculator?

Aug 30, 2016

$x = 2.916$

#### Explanation:

Log form and index form are interchangeable.

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

${\log}_{4} 57 = x \Leftrightarrow {4}^{x} = 57 \leftarrow$ (x is between 2 and 3)

The variable is in the index - use logs:

$x \log 4 = \log 57$

$x = \log \frac{57}{\log} 4$

$x = 2.916 \leftarrow$ (as we expected)

The same result would have been obtained from the change of base law.