Question

Use the Power Property of Logarithms to expand. Simplify if possible. (Assume the variable is positive.)

log4(x2)

Answer 1

The logarithm log4(x^2) can be expanded using the Power Property to 2 · log4(x), which indicates that the logarithm of x squared is twice the logarithm of x.

Step-by-step explanation:

To expand the logarithm log4(x2) using the Power Property of Logarithms, we apply the rule that states the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.

In this case, we have an exponent of 2 on the variable x within the logarithm.

The Power Property allows us to move the exponent to the front of the logarithm, which simplifies our expression to:

2 · log4(x)

This means that the logarithm of x2 base 4 is equivalent to twice the logarithm of x base 4.