Why is log₂(8) = 3? Why can’t you put negative numbers inside a logarithm? And what even is a log, beyond a formula your teacher told you to memorize? In this visual C-Infinity lesson, we trace logarithms back to where they actually come from: 👉 they are the inverse functions of exponentials. Once you see that relationship geometrically, everything clicks. Using clear animations, we walk through: 🔹The exponential function f(x) = aˣ and why it’s one-to-one 🔹How to construct its inverse f⁻¹(x) step by step 🔹Why that inverse must be the logarithm logₐ(x) 🔹Why log₂(8) = 3 becomes completely obvious 🔹Why logs only accept positive inputs 🔹How log graphs change as the base changes 🔹Why logs are actually extremely “well-behaved” functions (despite scary notation) By the end, logarithms will feel like basic algebra, not magic. ⸻ 📚 Continue Learning (Completely FREE) Take this concept further and practice interactively: 👉 Study the Log Lesson on DESMOS ⸻ 🌐 Want personalized academic support? Get 1-on-1 online tutoring from top international tutors at LightHouse Global — your academic partner for IB, College Application, and School Subjects. ⸻ 📐 C-Infinity We create visual, intuitive math explanations that actually make sense. ✨If you like math you can see, subscribe and join us for more! : @c-infinity Let us know in the comments if you want a follow-up video on log rules or other exponential/log topics! ⸻ 🎥 Chapters 0:00 — Why logs feel confusing (log₂8 = 3??) 0:33 — Exponential review: f(x) = aˣ 1:03 — Introducing the inverse function f⁻¹ 1:40 — f⁻¹(f(x)) = x and f(f⁻¹(x)) = x 2:08 — Building the log graph from the exponential 2:47 — Characteristics of the inverse function f⁻¹ 2:57 — Naming the inverse: the logarithm 3:50 — What counts as a “valid” base for logs? 4:16 — How the logarithm graph changes with the base 4:36 — Everything we now know about logs #logarithms #exponents #ibmath #inverse #inversefunctions #inversefunction #logarithm #highschoolmath #precalculus #mathhelp #mathanimation #maths #mathskills #mathsucks #mathstudent #ib #internationalbaccalaureate #ibdp #IGCSE #algebra #trigonometry #apmaths #education #mathtutorial #mathtutor #mathsmemes #dsemaths #mathstudents #mathsteacher #mathsisfun #gcsemaths #quickmaths #mathstutor #mathsclass #mathstricks #mathsjokes #brunomathsson #mathstations #mathslover #mathsproblems #mathsfun #alevelmaths #earlymaths #mathsquiz #mathsmeme #mathsmock #mathsnotes #mathsbeauty #ilovemaths #lovemaths #addmaths