How do you solve the expression log4y + 9 log4(4) + log4(64)?

To solve the expression log₄y + 9 log₄(4) + log₄(64), we’ll break it down step by step:

Step 1: Simplifying Each Term

1. The term log₄(4) is equal to 1 because any logarithm of a number to itself is 1. Therefore:

• log₄(4) = 1

2. We can now simplify the expression:

• 9 log₄(4) = 9 * 1 = 9

Step 2: Simplifying log₄(64)

The next term, log₄(64), can be simplified. We know that:

• 64 = 4³

Thus:

• log₄(64) = log₄(4³) = 3

Step 3: Combine All Terms

Now we can rewrite the original expression:

• log₄y + 9 + 3

This simplifies to:

• log₄y + 12

Final Answer

The simplified form of the expression log₄y + 9 log₄(4) + log₄(64) is:

log₄y + 12