Visual Lesson
Logarithms
A logarithm just answers one question: how many times do you multiply the base to reach the value? Watch it count — and see what a log scale really shows.
How many times do you multiply 10 to reach 1?
The circle counts your ×10 steps; the number under it is the value so far.
Where does 1 sit on each ruler?
Linear scale
Equal steps of size — so 1, 10, 100… crowd together at the start.
Log scale
Equal multiplies — every ×10 is the same-size jump, so the powers line up evenly.
That even spacing is exactly what a logarithm measures: position on a log scale = the exponent.
The exponent sets the value 10³ = 1,000, so log₁₀(1,000) = 3 comes out exact.
What is a logarithm?
A logarithm is the inverse of an exponent. Where bᶜ = x asks “what do you get when you multiply the base b by itself c times?”, the logarithm logb(x) = c asks the reverse: “how many times do you multiply b to reach x?” They are two ways of writing the same fact. For example, 10³ = 1,000 and log₁₀(1,000) = 3 say exactly the same thing.
How to use this tool
- Pick a base (2 or 10) and an exponent from 0 to 6. The value is always the base raised to that power, so the logarithm comes out to a whole number.
- Press Play to multiply the base one step at a time — 1 → b → b² → … — counting each multiplication out loud until you land on the exponent.
- Read the matched pair beneath the animation: the exponent form and the logarithm form update together so the inverse relationship stays in view.
- Watch the same value on a linear scale and a log scale: on the log scale, each ×10 is one even jump — which is why 1, 10, 100, 1,000, and 10,000 are spaced equally.
Why a log scale helps
On a linear ruler, small numbers pile up near the start and huge numbers run off the end. A log scale turns every multiplication into an equal step, so quantities that span many orders of magnitude — earthquakes, sound, pH, star brightness, page views — fit on one readable axis. Seeing a value’s position be its exponent is the intuition that makes logarithms click.
Good for
Grade 8 through high school: introducing logarithms in pre-algebra and Algebra 2, reviewing for precalculus, and building the number sense behind exponential growth and log scales.
Bring it to a lesson
These tools pair with the full curriculum — guided lessons that teach each concept, then send you here to see it and practice.