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Logarithm Calculator

Choose what you want to find: the log result, the power value, or the missing base. The calculator keeps base, value, and exponent labels visible so the formula is easy to follow.

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Logarithm solver

Log result y

3.00

Equation

log_10(1,000) = 3.00

Use base and value to find the exponent.

What do you want to find?

Start with the question, then adjust the three related numbers below.

Quick examples

Tap a familiar case to see how the numbers connect.

Base, value, exponent

In log_b(x) = y, b is the base, x is the value, and y is the exponent.

Related results

Log result y

3.00

log_10(1,000) = 3.00

Power value x

1,000

10^3 = 1,000

Solved base b

10.00

1,000^(1 / 3) = 10.00

Common log views

Common log log10(x)3
Natural log ln(x)6.9078
Binary log log2(x)9.9658
Reciprocal log log_x(b)0.3333

Nearby power table

ExponentValue
010^0 = 1
110^1 = 10
210^2 = 100
310^3 = 1,000
410^4 = 10,000

Power scale

See whether the value is closer to the lower or upper exact power.

Lower power

10^2

100

Upper power

10^3

1,000

How logarithms work

A logarithm answers one question: how many times should the base be multiplied to reach the value? If log10(1000) = 3, it means 10^3 = 1000.

Usage notes

  • log_b(x) = y means b^y = x.
  • Change of base: log_b(x) = ln(x) / ln(b).
  • To solve the base: b = x^(1 / y), when x > 0 and y is not 0.

Frequently asked questions

What is the difference between log and ln?expand_more

log usually means base 10 in many calculators, while ln always means the natural log with base e.

Why can the base not be 1?expand_more

Multiplying 1 by itself never changes the value, so it cannot describe a useful power relationship.

Can logarithms use decimals?expand_more

Yes. Decimal bases and values are common in growth, decay, science, finance, and data scale calculations.

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