Evaluate \(\frac{log_5 (0.04)}{log_3 18 – log_3 2}\)

Explanation

\(\frac{log_5 0.04}{log_3 18 - log_3 2}\)

= \(\frac{log_5 0.04}{log_3(\frac{18}{2})}\)

= \(\frac{log_5 0.04}{log_3 9}\)

= \(\frac{-2}{2}\)

= -1

Let log₅ 0.04 = x

5x = 0.04

x = \(\frac{4}{100}\) = 5^-2

Let log₃ 9 = z

3² = 3²

z = 3