Question
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Evaluate the expression without using a calculator.

Ask by Evans Delgado. in the United States
Mar 23,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The expression evaluates to 4.

Solution

We start with the expression:
Using the logarithm property that states:
with and , we have:

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Simplify this solution

Extra Insights

Did you know that logarithms are essentially the opposite of exponentials? So when you see , you’re basically asking, “To what power do I need to raise 2 to get ?” The answer? It’s simply 4!
Logarithms can also be really handy in real-world applications, like in computer science for algorithmic complexity or in finance for calculating growth rates. They help in simplifying complex calculations, like determining the scale of exponential growth in various fields, from population studies to any scenario involving exponential decay or growth. Isn’t math just an amazing tool for understanding the world?

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