Interactive logarithmic function reflection visualisation

Logarithms are just exponentials reflected

Every exponential curve has a mirror twin — flip it across y = x and you get its logarithm. The base controls how steeply both curves rise. Raise the base and watch the two dots stay mirror images of each other.

Reflection visualiser
Base = 2.0
Raise the base. Watch where the two dots sit either side of y = x.
y = 2.0ˣ ⟷ y = log₂(x)
Base value
1.1 3.0 5.0
Point on y = aˣ
(1, 2.0)
Reflected on y = log_a(x)
(2.0, 1)

The product law says log(mn) = log m + log n. Multiplication inside the log becomes addition outside. This happens because logs are exponents — when you multiply powers of the same base, you add their exponents. For example, log(8 × 4) = log 8 + log 4 because 2³ × 2² = 2⁵. The log converts the product back into a sum of exponents, which is why logs turn multiplication into addition.

Know This
A logarithm is the inverse of an exponential, so log_a(x) and a^x are reflections in y = x, with a vertical asymptote at x = 0 and passing through (1, 0).