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

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Answer 1 · 2016-11-13T17:01:30

$log_3 42=3.4022$

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

$xlog3=log42$ and hence $x=log42/log3=1.6232/0.4771=3.4022$

Hence $log_3 42=3.4022$

Answer 2 · 2016-11-13T17:09:56

$log_3 42$

Expand it into prime factors:
$=log_3 3 + log_3 14$
$=1+log_3 14$

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