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

##### 1 Answer

Feb 1, 2018

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 #