Expand the logarithm: log_3⁡ 12x^3 y^2 ⁡.

Question

Please show work/ calculation as needed

Answer 1

log₃ 12x³ y² = log ₃ (12x³) + log₃ (y²) = log₃ (12) + log₃ (x³) + 2 log₃ (y)

= log₃ (12) + 3 log₃ (x) + 2 log₃ (y)

Using the log rules

log₃ (ab) = log₃ (a) + log₃ (b)

log₃ (a^b) = b log₃ (a)