Simplify 2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9

A.

1 - 4 log3

B.

-1 + 2 log 3

C.

-1 + 5 log2

D.

1 - 2log 2

Correct answer is D

2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9

[\(\frac{2}{5}\))2 x 9] = log \(\frac{4}{25}\) x \(\frac{9}{1}\) x \(\frac{125}{72}\)

= log \(\frac{72}{125}\)

= log \(\frac{5}{2}\)

= log \(\frac{10}{4}\)

= log 10 - log 4

= log10 10 - log10 22

= 1 - 2 log2