how to use log on calculator

What does “log” mean on a calculator?

When people ask how to use log on a calculator, they are usually asking how to find an exponent. A logarithm answers this question: “To what power do I raise the base to get this number?”

• log₁₀(1000) = 3 because 10³ = 1000
• ln(7.389...) = 2 because e² = 7.389...
• log₂(64) = 6 because 2⁶ = 64

Logs show up in chemistry (pH), sound (decibels), earthquakes (Richter scale), finance (continuous growth), machine learning, and many algebra classes.

The two main log buttons: LOG and LN

LOG button

The LOG key is usually base 10. So typing LOG 1000 gives 3.

LN button

The LN key is natural log, base e (approximately 2.71828). So typing LN e gives 1, and LN 1 gives 0.

• Use LOG when your base is 10.
• Use LN when your equation involves e or continuous growth/decay.

How to use LOG (base 10) step by step

• Step 1: Turn on scientific mode if needed.
• Step 2: Press the LOG key.
• Step 3: Enter the number (must be positive).
• Step 4: Press = (or close parenthesis then =, depending on model).

Example: Find log₁₀(250)

• Key sequence: LOG 250 =
• Result: about 2.39794

How to use LN (natural log) step by step

• Step 1: Press the LN key.
• Step 2: Enter your positive number.
• Step 3: Press =.

Example: ln(5)

• Key sequence: LN 5 =
• Result: about 1.60944

How to compute logs with any base (like log₂ or log₅)

Many calculators do not have a dedicated log base b button, but you can still compute it using the change-of-base formula:

logᵦ(x) = ln(x) / ln(b) (or log(x)/log(b), same idea)

Example: log₂(64)

• Type: LN 64 ÷ LN 2 =
• You get: 6

Example: log₅(125)

• Type: LN 125 ÷ LN 5 =
• You get: 3

Important rules you should remember

• You can only take logs of positive numbers.
• log(1) = 0 in every valid base.
• log(base) = 1 (example: log₁₀(10)=1, ln(e)=1).
• If 0 < x < 1, the log result is negative.
• Base must be positive and cannot be 1.

Inverse keys: 10ˣ and eˣ

Logarithms are inverse operations of exponents. That is why calculators often pair these keys:

• LOG pairs with 10ˣ
• LN pairs with eˣ

If you calculate LOG(500) and get about 2.6990, then 10^2.6990 should return about 500 (small rounding differences are normal).

Common mistakes and how to fix them

1) “Math Error” appears

• You likely entered 0 or a negative number into log/ln.
• Fix: Use positive input only.

2) Wrong mode or misplaced parentheses

• Some calculators need parentheses like LOG(250).
• Fix: Enter exactly as your model expects and close brackets.

3) Using LOG when the formula requires LN

• In growth models with e, you usually need LN.
• Fix: Match the log type to the equation’s base.

4) Rounding too early

• Intermediate rounding can shift final answers.
• Fix: keep full calculator precision until the final step.

Practice problems

Try these on your calculator:

• log₁₀(100000) = ? (Answer: 5)
• ln(1) = ? (Answer: 0)
• log₂(32) = ? (Answer: 5)
• log₃(1/9) = ? (Answer: -2)

Quick exam strategy

• Read the base carefully before pressing a key.
• If base isn’t 10 or e, use change-of-base immediately.
• Estimate first: this helps catch button mistakes.
• Use memory/ANS keys for multi-step expressions.

Final takeaway

To use log on a calculator confidently, remember this simple map:

• LOG = base 10
• LN = base e
• Any other base = ln(x) / ln(base)

Use the interactive calculator above whenever you want to check answers or practice quickly.