Final answer:
To evaluate the expression log₄ 16¹⁰⁰, we need to find the logarithm of 16 to the base 4. Using the property of logarithms, we simplify the exponent of 16¹⁰⁰ to 100log₄ 16. Evaluating this expression gives us a result of 200.
Step-by-step explanation:
To evaluate the expression log₄ 16¹⁰⁰, we need to understand the properties of logarithms. In this case, we have a logarithm with a base of 4 and an argument of 16¹⁰⁰. The exponent of 16¹⁰⁰ can be simplified by using the property of logarithms that states logₐ bᶻ = zlogₐ b. Applying this property, we get 100log₄ 16. Now, let's evaluate the expression.
To evaluate 100log₄ 16, we need to find the logarithm of 16 to the base 4. In other words, we need to find the exponent to which 4 is raised to get 16. Since 4 raised to the power of 2 gives us 16 (4² = 16), the logarithm of 16 to the base 4 is 2. Therefore, 100log₄ 16 can be simplified to 100(2) = 200.
So, the evaluation of the expression log₄ 16¹⁰⁰ is 200.