# How do you simplify #1/2 ln (4t^4) - ln 2#?

##### 1 Answer

This is asking you to remember the properties of logarithms. Here are the ones you need to know:

#\mathbf(lna^b = blna)# #\mathbf(clna - clnb = cln\frac(a)(b))#

So, we can start by getting that exponent out in front:

#1/2ln4t^4 - ln2#

#= 1/2ln(2t^2)^2 - ln2#

Be careful that you do the above step correctly. It would be *incorrect* to change *only* applied to the

(If you did, you would imply that the expression was

Now, the exponent applies to the **quantity**

#= cancel(1/2)*cancel(2)ln2t^2 - ln2#

#= ln2t^2 - ln2#

With the same coefficients

#= ln\frac(cancel(2)t^2)(cancel(2))#

#= lnt^2#

#= color(blue)(2lnt)#