How to use this calculator
A real logarithm requires a positive argument. A horizontal shift therefore moves the domain boundary and vertical asymptote. The base controls the direction and scale of growth, while A and k apply vertical transformations. The change-of-base identity makes the computation work for any supported base.
The method
Enter the values in the labeled fields, check the units or selected mode, and choose Calculate. The result includes the applicable working and a breakdown or visual when useful. Change an input and calculate again to update the result.
Logarithm base: 10 Vertical scale A: 1 Horizontal shift h: 0 Vertical shift k: 0 Domain width to show: 10
Logarithmic graph: y = 1 log_10(x - (0)) + (0)
Real domain: x > 0.
Scope and limitations
Only the specified transformed logarithmic form is supported. The base must be positive and not equal to 1. Values at or left of the domain boundary are not plotted.
Common questions
Can the base be between 0 and 1?
Yes. Such logarithms are defined for positive arguments and decrease as the argument grows before any additional vertical transformation.
Why is the left boundary excluded?
At x = h the argument is zero, and a real logarithm of zero is undefined.
References & further reading
External references provide background, not an endorsement of this implementation. See our methodology for numerical conventions and limitations.