How do you simplify the expression 5 log2 k + 8 log2 m + 10 log2 n?

To simplify the expression 5 log₂ k + 8 log₂ m + 10 log₂ n, we can make use of the properties of logarithms. The first step is to factor out the common logarithmic base, which is base 2 in this case.

We can rewrite each term using the power rule of logarithms, which states that:

n log_b a = log_b aⁿ

Applying this rule:

• 5 log₂ k = log₂ k⁵
• 8 log₂ m = log₂ m⁸
• 10 log₂ n = log₂ n¹⁰

Now we can rewrite the entire expression as:

log₂ k⁵ + log₂ m⁸ + log₂ n¹⁰

Next, we can combine these logarithmic terms using the property that says:

log_b a + log_b c = log_b (a * c)

This gives us:

log₂ (k⁵ * m⁸ * n¹⁰)

So, the simplified form of the expression 5 log₂ k + 8 log₂ m + 10 log₂ n is:

log₂ (k⁵ * m⁸ * n¹⁰)