The calculator evaluates a logarithm or the matching exponential. You choose the direction, then enter the base and the second number. The steps recall that y = log_b(x) means b^y = x.
Evaluate
Lesson: logarithm and exponential as inverses
A logarithm answers the question “what exponent produces this number?” The exponential puts that exponent back on the base and recovers the original number. The two functions undo each other when the base is valid: greater than 0 and not equal to 1.
The calculator evaluates a logarithm with a change of base, ln(x) / ln(b). That is an arithmetic convenience. It is the same value as log_b(x). An argument that is 0 or negative is outside the domain of a real logarithm, so the calculator reports an error instead of a number.
Practice problems
1. Common log
Evaluate log10(1000).
2. Inverse check
Evaluate 25, then log2 of that result.
3. Outside the domain
What happens if the argument is −4?
Show answers
Problem 1. The value is 3, because 10³ = 1000.
Problem 2. 2⁵ = 32, and log₂(32) = 5.
Problem 3. The calculator reports that the argument must be greater than 0.