If loga270 – loga10 + loga (frac{1}{3}) = 2, what is the value of a?

If log_a270 – log_a10 + log_a (frac{1}{3}) = 2, what is the value of a?

Correct Answer: Option A

Explanation

log_a270 – log_a10 + log_a(frac{1}{3}) = 2
log_a270 + log_a(frac{1}{3}) – log_a10 = 2
log_a(270(frac{frac{1}{3}}{10})) = 2
log_a9 = 2
a^a = 9
a = (sqrt{9}) = 3