ZovaTool

Log Calculator

Result

log_10(1000)
3
log₁₀(1000)
3
ln(1000)
6.907755
log₂(1000)
9.965784
Antilog (b^result)
1000
Mantissa / Char.
2 . 1

Step-by-step (change of base)

Step 1
log_b(x) = ln(x) / ln(b)
Step 2
ln(1000) = 6.907755, ln(10) = 2.302585
Step 3
= 6.907755 / 2.302585 = 3
Step 4
Verify: 10^3 = 1000

Log properties

  • log(a·b) = log a + log b
  • log(a/b) = log a − log b
  • log(a^n) = n · log a
  • log_b(b) = 1
  • log_b(1) = 0
  • Change of base: log_b(x) = log_k(x) / log_k(b)

How to use the Log Calculator

  1. Enter the argument x (must be positive).
  2. Enter a base b (positive, ≠ 1). Use 10 for common log, e for natural log.
  3. Quick-pick base 2, 10, or e buttons available.
  4. Step-by-step shows the change-of-base computation.
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Logarithms in plain English

log_b(x) answers the question 'what power do I raise b to so I get x?' For example log_2(8) = 3 because 2^3 = 8.

The change-of-base identity log_b(x) = ln(x)/ln(b) lets you compute any logarithm using only natural log — which is exactly what this calculator does internally.