Question
Which logarithm is equal to \( 2 \ln 10 ? \)
Ask by Newton Johnson. in the United States
Mar 01,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
2 ln 10 is equal to ln 100.
Solution
Recall the power rule of logarithms: a ln(x) = ln(xᵃ). Using this rule, we have:
2 ln 10 = ln(10²) = ln 100.
So, 2 ln 10 is equal to ln 100.
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Simplify this solution Mind Expander
Did you know that the logarithm you're looking for can be expressed in terms of base 10? Specifically, \( 2 \ln 10 \) can be rewritten using the change of base formula. This means you can express it as \( \ln(10^2) \) or \( \ln(100) \). Now, here's a fun fact about logarithms: they are deeply intertwined with many areas of science and technology! For instance, the Richter scale for measuring earthquakes uses a logarithmic scale, meaning that a magnitude 6 earthquake is ten times more powerful than a magnitude 5! This shows just how crucial logarithms are in understanding big changes in the world around us.
