Question

Solve the logarithm: log₂(x²) = 8.

Answer 1

To solve log₂(x²) = 8, we use the property that logarithm of a number raised to an exponent is the exponent times the logarithm of the base number. Simplifying, we get x = 16 as the solution.

Step-by-step explanation:

To solve the equation log₂(x²) = 8, we'll use a logarithmic property that states the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.

First, we can express the given equation using the property mentioned:

1. log₂(x²) = 8 becomes 2×log₂(x) = 8 (because log₂(x²) = 2×log₂(x)).

Next, divide both sides by 2 to isolate the logarithm:

1. log₂(x) = 4

Now convert from logarithmic to exponential form to solve for x:

1. 2⁴ = x, so x = 16

The solution to the original equation is x = 16.