Question

Log₃9
Expand each logarithm as much as possible.

Answer 1

To expand the logarithm log₃9, we recognize that 9 is 3 squared and use the property of logarithms to simplify log₃(3^2) to 2 * log₃(3). Since log₃(3) equals 1, the final answer is 2.

Step-by-step explanation:

The question asks to expand the logarithm log₃9. To expand this logarithm, we can use the property of logarithms that states the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. Since 9 is 3 squared (3^2), we can write this as:

log₃(3^2)

Using the aforementioned property, we can simplify this logarithm to:

2 × log₃(3)

Now, as the base of the logarithm and the number inside the logarithm are the same (both 3), we can simplify this further since log₃(3) equals 1:

2 × 1 = 2

Thus, the expanded form of log₃(9) is simply 2.