ln vs log: What's the Difference? (Explained Simply)

When you're learning logarithms, you often see two different terms: ln and log. While they look similar, they mean different things! In this article, we'll break it down in the simplest way possible so you can understand the difference once and for all.

📌 What is a Logarithm?

A logarithm is the inverse of exponentiation. It answers the question:

If \( a^x = b \), then \( \log_a(b) = x \)

For example: \[ \log_2(8) = 3 \quad \text{because } 2^3 = 8 \]

🔹 What is log?

In most textbooks and calculators:

• log means common logarithm
• Its base is 10

So,

\[ \log(x) = \log_{10}(x) \]

For example: \[ \log(1000) = 3 \quad \text{because } 10^3 = 1000 \]

🔹 What is ln?

ln means natural logarithm. Its base is a special irrational number called e, which is approximately:

\[ e \approx 2.71828 \]

So:

\[ \ln(x) = \log_e(x) \]

Example: \[ \ln(e^2) = 2 \quad \text{because } e^2 = e^2 \]

🧠 Key Differences Between ln and log

✨ Fun Fact: Why is ln Used So Much in Calculus?

The number \( e \) has unique properties in calculus:

• The derivative of \( \ln x \) is \( \frac{1}{x} \)
• The function \( e^x \) is its own derivative!

These properties make \( \ln \) and \( e \) essential in growth/decay models, compound interest, and calculus-based problems.

📚 Still Confused? Learn Logarithms Visually!

If you want to master logs visually with examples and animations, check out this amazing guide:

🔍 Click Here to Learn Logarithms the Easy Way

🔖 Tags:

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