ln or log: which button solves your problem?
Logarithms recover an exponent. The right button depends on the base, not on how large the input looks.
Scientific calculator →Read the base first
On this calculator, log means base 10 and ln means base e. Because 10³ = 1000, log(1000) = 3. Because e² has exponent 2, ln(exp(2)) = 2 apart from possible rounding. An expression written as log in a textbook may use another convention, so check the definition in that course or document.
Solve a growth question
Suppose a hypothetical amount multiplies by 1.08 each complete period. Reaching twice the start requires 1.08^t = 2, so t = ln(2)/ln(1.08), approximately 9.006 periods. If changes happen only at whole-period boundaries, the first completed period at or above twice the start is period 10. This model assumes the multiplier never changes and no money enters or leaves.
Other bases and invalid inputs
For a positive x and a positive base b other than 1, log base b of x equals ln(x)/ln(b). Thus ln(32)/ln(2) = 5. Real logarithms of zero and negative numbers are undefined; adding parentheses cannot fix that domain problem. Also, ln(a+b) is not generally ln(a)+ln(b). Keep the original expression grouped and round only the final answer. In the doubling example, using log(2)/log(1.08) gives the same result because the base-change factor cancels in the ratio.
Try the calculators
- Scientific calculator
Arithmetic, powers, trigonometry and logarithms.
- Quadratic equation
Solve for real or complex roots.
- Triangle calculator
Calculate area and perimeter from three sides.