Question

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

Answer 1

`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

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

Hence `log_3 42=3.4022`

Answer 2

`log_3 42`

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