doomath Calculator
Logarithm & Change of Base Calculator
Evaluate logarithms with arbitrary base, natural log ln(x), common log log10(x), binary log log2(x), and verify exponential equivalence.
InputsChange a value to recalculate instantly
ResultUpdates as you type
FORMULA & STEPSLogarithm & Change of Base Calculator — Mathematical Derivation & Steps
2 StepsSequential Calculation Breakdown
1
Check domain
x > 0, b > 0 and b ≠ 1.
2
Change of base
Divide natural logarithms to evaluate the requested base.
λ DooMathWork with this calculation
Local · deterministic · optionalQuick mathNatural-language-style shortcuts for deterministic arithmetic.
Calculator guide
How to use the Logarithm & Change of Base Calculator
Evaluate logarithms with arbitrary base, natural log ln(x), common log log10(x), binary log log2(x), and verify exponential equivalence.
01Set inputsChoose values, units and assumptions.
02Apply the modellog_b(x) = ln(x) / ln(b); log_b(xy) = log_b(x) + log_b(y); log_b(x^k) = k log_b(x)
03Read the resultCheck the output against the assumptions before using it.
What this calculator does
Enter the logarithmic base b and positive argument x. The calculator applies the change of base theorem, computes common and natural logs, and checks b^y = x.
Formula & method
log_b(x) = ln(x) / ln(b); log_b(xy) = log_b(x) + log_b(y); log_b(x^k) = k log_b(x)
Assumptions & notes
- The logarithm is the inverse operation of exponentiation.
- The natural logarithm has base e ≈ 2.71828.
- Logarithmic functions grow slower than any positive power of x.