Simplify 5 log₂ k - 8 log₂ m + 10 log₂ n.

Solution:

Given expression is

5 log₂ k - 8 log₂m + 10 log₂n.

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

= log₂ k⁵ - log₂ m⁸ + log₂ n¹⁰

= log₂ k⁵ + (log₂ n¹⁰ - log₂ m⁸)

= log₂ k⁵ + log₂( n¹⁰/ m⁸)

= log₂ {k⁵ × n¹⁰ / m⁸}

Simplify 5 log₂ k - 8 log₂m + 10 log₂n.

Summary:

5 log₂ k - 8 log₂m + 10 log₂n is simplified as log₂ {k⁵ × n¹⁰ / m⁸}.