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: Option D
Explanation
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
= log_{10} 10 – log_{10} 22
= 1 – 2 log2