Question #7d8c4

1 Answer
Jun 5, 2017

Answer:

I got

#log[(16/3)*(2/9)]#

Explanation:

We know the properties of log:

#log a + log b = log (a*b)#

#log a - log b = log(a/b)#

#a log b = log b^a#

We have:

#(-log 3 + 2 log 4) - (- log 2+ 2 log 3)#

Rearranging

#(2 log 4 - log 3)-(2 log 3 -log 2)#

Applying properties, solving parentheses first

#(log 4^2 - log 3)-(log 3^2 - log 2)#

#[log(4^2/3)]-[log(3^2/2)]#

#[log(16/3)]-[log(9/2)]#

Again it is of the form #log a- log b#

#log((16/3)/(9/2))#

Simplifying

#log[(16/3)*(2/9)]#