Question #7d8c4

1 Answer
Jun 5, 2017

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)]