What is a logarithm?
A logarithm answers: to what power must the base be raised to get this number? log base 2 of 8 is 3, because 2 raised to the power 3 is 8.
// maths › Algebra
Logarithm calculator
Logarithm of a value to any base, with the log curve plotted.
log_b(x) = ln(x) / ln(b)
A mind behind this: John Napier 1550–1617
Frequently asked questions
How do I compute a log to any base?
Use the change-of-base rule: log_b(x) = ln(x) / ln(b). This lets a calculator find a log to any base using natural logs.
What is the difference between ln and log?
ln is the logarithm to base e (about 2.718), used widely in calculus and growth problems. 'log' usually means base 10 unless a base is given.
Where is this used in real life?
Earthquakes — the Richter scale is base-10 logarithmic, so magnitude 6 is ten times stronger than 5. Sound — decibels measure loudness on a log scale. Acidity — pH is the negative log of hydrogen-ion concentration. Computing — log base 2 counts how many times you can halve a list, which is why searching a sorted list is fast.
How does the graph help me understand logs?
The dashed guide lines trace your value up to the curve and across to the answer, so you can literally read log_base(value) off the y-axis.