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