log_b(x) is the inverse of b^x. Their graphs are mirror images across the line y = x — swap each point’s coordinates.

— f(x) = b^x (asymptote y = 0)
— f⁻¹(x) = log_bx (asymptote x = 0)

Base b = 2

f(x) = 2ˣ

f⁻¹(x) = log₂ x

base b 2

point x 1

Try: slide the base below 1 (e.g. b = 0.5) — the exponential now decays and its log inverse flips, but both still mirror across y = x.