How this calculator works
Exponential and logarithmic equations describe the same relationship from different directions. Choose a positive base other than one. Number mode finds the exponent with a logarithm, which need not be an integer. Equation modes use the entered exponent or logarithm value to calculate the matching number. This is a base-power representation rather than scientific notation.
Formula
b^a = c if and only if log_b(c) = a, where b > 0, b != 1 and c > 0.
Worked example
100 = 10^2 becomes log_10(100) = 2. The equation 2^5 = 32 is equivalent to log_2(32) = 5.
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Frequently asked questions
Does every number have an integer exponent?
No. For instance, 3 is 2 raised to approximately 1.5849625.
Is this scientific notation?
Scientific notation uses a coefficient times a power of ten. This tool expresses the entire positive number as a power of the selected base.
Can I enter zero?
Zero is not a finite real power of a positive base and has no real logarithm, so it is rejected.