Question

Solve `2ln 4 - 2ln(1/2)`?

Answer 1

Firstly a terminology primer, we solve equations but we simplify expressions.

Using the logarithm property:

`log a^b = bloga`

We can simplify the given expression as follows

`2ln 4 - 2ln(1/2) = 2ln 2^2 - 2ln(2^(-1))`
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 2(2)ln 2 - 2(-1)ln2`
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 4ln 2 +2ln2`
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 6ln2`