📐 Math
Log Calculator
Calculate the logarithm of a number to a specified base. Logarithms are the inverse operations to exponentiation, answering 'to what power must the base be raised to produce a given number?'.
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Formula
y = log_b(x) ⇔ b^y = xb- The base (must be positive and not equal to 1)
x- The argument (must be positive)
y- The resulting logarithm
Example
Calculating a Base-2 Logarithm
Find log_2(32).
- Set the base b = 2 and argument x = 32.
- Ask: 2 raised to what power equals 32?
- Since 2 × 2 × 2 × 2 × 2 = 32, we know 2^5 = 32.
- Result: log_2(32) = 5.
Frequently Asked Questions
If your physical calculator only has 'log' (base 10) or 'ln' (base e), you can calculate any base using the formula: log_b(x) = log(x) / log(b). Our calculator handles this internally for you.