Last updated: April 2026
log[2](8) = ?
3
Verification: 2^3 = 8
log_b(x) = log(x) / log(b) = ln(x) / ln(b)
log_b(xy) = log_b(x) + log_b(y)
log_b(x/y) = log_b(x) - log_b(y)
log_b(x^n) = n x log_b(x)
log_b(b) = 1
log_b(1) = 0
A logarithm asks what power you raise a base to in order to get a value.
Common log uses base 10. Natural log uses base e, which is central to growth and decay.
Logarithms are used in science, finance, pH, decibels, computing, statistics, and exponential growth models.
This calculator is designed to help you understand the likely number before you make a decision or start an application.
Your result should be checked against official UK guidance, especially if your circumstances include dependants, exemptions, prior leave, or a complex immigration history.
Treat the figure as a planning tool rather than legal advice. Where the answer affects an application deadline or major payment, speak to an authorised adviser.
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