write 5-log2(4y) as a single quantity

assuming log2 (4y) means log2 (4y)

I could write 5 as log2 32

so we have:
5 - log2 (4y)
= log2 32 - log2 (4y)
= log2 (32/(4y))
= log2 (8/y)

To simplify the expression 5 - log2(4y), we can start by using the logarithmic property log(a) - log(b) = log(a/b):

5 - log2(4y) = 5 - [log2(4) + log2(y)]

Next, we simplify the logarithms:

5 - [log2(4) + log2(y)] = 5 - [2 + log2(y)]

Since log2(4) = 2 (because 2 raised to the power of 2 equals 4), we have:

5 - [2 + log2(y)] = 5 - 2 - log2(y) = 3 - log2(y)

So, 5 - log2(4y) simplifies to 3 - log2(y).

To write 5 - log2(4y) as a single quantity, we can simplify the expression using logarithmic properties. The problem can be approached as follows:

Step 1: Apply the logarithmic rule logb(xy) = logb(x) + logb(y) to the expression log2(4y).
- log2(4y) can be rewritten as log2(4) + log2(y).

Step 2: Simplify log2(4) using logarithmic rules.
- 2^2 = 4, so log2(4) = 2.

Step 3: Combine the terms.
- 5 - log2(4y) = 5 - (2 + log2(y))
- Since there is a negative sign, we can rewrite it as 5 - 2 - log2(y).
- 5 - 2 = 3, so the expression becomes 3 - log2(y).

Therefore, the simplified form of 5 - log2(4y) is 3 - log2(y).