Proof: A(log B) = log (B^A), log A - log B = log (A/B)

Proofs of the logarithm properties: A(log B) = log (B^A) and log A - log B = log (A/B)

Lets see if we can stumble our way

to another logrithm property

So lets say that

Oh, I dont know

Lets say that

log base x of A

is equal to B, right?

That's the same thing as saying

That's the exact same thing as saying that

x to the B is equal to A

Fair enough

What I want to do is experiment - what happens if I multiply this expression by another variable - let's call it C

Right, so I'm going to multiply both sides of this equation by C

I'm going to switch colours just to keep things interesting

That's not an X that's a dot - times C

So I'm going to multiply both sides of this equation by C

So I get C times log base X of A is equal to

(multiply both sides, right?)

is equal to B times C

Fair enough.