Simplify 7 log₃ k + 6 log₃ m - 9 log₃ n.

Solution:

Given expression: 7 log₃ k + 6 log₃ m - 9 log₃ n

We have logarithmic properties when bases are equal.

1. log_a(x) - log_a(y) = log_a(x/y)
2. log_a(x) + log_a(y) = log_a(xy)
3. log_ax^m = mlog_ax

log₃k⁷+ log₃m⁶ - log₃n⁹

= log₃k⁷ + (log₃m⁶ - log₃n⁹)

= log₃k⁷+ log₃(m⁶/n⁹)

= log₃{k⁷ × m⁶ / n⁹}

Simplify 7 log₃ k + 6 log₃ m - 9 log₃ n.

Summary:

7 log₃ k + 6 log₃ m - 9 log₃ n is simplified as log₃{k⁷ × m⁶ / n⁹}