Online logarithm calculator: enter the base a and number N to find log_a N (the power to which a must be raised to give N), with change-of-base steps. Logarithms invert exponentiation.
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a^x=N ⇔ x=log_a N
a>0, a≠1
Must be positive N>0
📖 Tutorial | Logarithm
1. Definition
If a^x=N (a>0,a≠1,N>0), then x is the logarithm of N to base a, written x=log_a N; a is the base and N the argument.
2. Formula & Notation
a
Base (a>0,a≠1)
N
Argument (N>0)
log_a N
The exponent x
3. Properties & Laws
a^(log_a N)=N and log_a(a^x)=x;
log_a 1=0, log_a a=1;
Base 10 is lg N, base e is ln N;
Negative numbers and 0 have no logarithm.
4. Steps
Enter the base a and number N;
Click "Find log";
Or click "Load Example".
5. Worked Examples
Example: Find log₂8. Since 2³=8, log₂8=3.
6. Common Pitfalls
The argument must be positive; The base needs a>0 and a≠1; The result is an exponent, not the number.
❓ FAQ | Logarithm
What is a logarithm?
The inverse of exponentiation: the power giving N.
Parts?
Base a, argument N, value log_a N.
Why must N be positive?
Powers of a positive base are positive.
lg and ln?
Bases 10 and e.
log_a 1, log_a a?
0 and 1.
On a calculator?
Use ln N/ln a.
Uses?
Exponential equations, orders of magnitude, pH, Richter.