Show that log₃ 9 + log₃ 3 = log₅ 125

Given: log₃ 9 + log₃ 3 = log₅ 125

Taking L.H.S:

= log₃ 9 + log₃ 3

= log $\dfrac{9}{3}$ + log $\dfrac{3}{3}$

= log $\dfrac{3^2}{3}$ + log $\dfrac{3}{3}$

= 2log $\dfrac{3}{3}$ + log $\dfrac{3}{3}$

= 2 x 1 + 1

= 2 + 1

= 3

Taking R.H.S.:

= log₅ 125

= log $\dfrac{125}{5}$

= log $\dfrac{5^3}{5}$

= 3log $\dfrac{5}{5}$

= 3 x 1

= 3

Thus, L.H.S. = R.H.S.

Hence, log₃ 9 + log₃ 3 = log₅ 125.