# How do you express log_3 42 in terms of common logs?

Nov 13, 2016

${\log}_{3} 42 = 3.4022$

#### Explanation:

Common logs means logarithm with base a $10$.

Here we have been given base $3$, so let us convert it to base $10$

Let ${\log}_{3} 42 = x$, then ${3}^{x} = 42$

and taking logarithm to base $10$ on both sides, we get from tables

$x \log 3 = \log 42$ and hence $x = \log \frac{42}{\log} 3 = \frac{1.6232}{0.4771} = 3.4022$

Hence ${\log}_{3} 42 = 3.4022$

Nov 13, 2016

${\log}_{3} 42$

Expand it into prime factors:
$= {\log}_{3} 3 + {\log}_{3} 14$
$= 1 + {\log}_{3} 14$