If x is equal to log base, I don't know, base b of a, that is equal to log base 10 of a, lowercase a, divided by log base 10 of b.

It either has log base, you know base 10, or base e, right?

Log of base a of b is equal to log base x of b divided by log base x of a.

That is the base.

Let's say log base three of I don't know log base three of well you know, let's make it interesting log base three of one nine minus log base three of eighty one.

log base 10 of 100 divided by log base 10 of 5.

So let's say I have log base B of A is equal to log base C of A divided by log base C of B.

log base 3 of 27 times x I'll write it that way is equal to log base 3 of 27 plus log base 3 of x.

So this is log base b of a minus log base b of c is equal to log base b of well I ran out.

That is equal to log base x of a minus log base x of b

When I took a negative number, and we call this the base, when the base is negative, in this case, negative four, and I raise it to an even power,

And those form the basis.

We'll just do it the with the number 3.

So I immediately take the reciprocal of the base.

This is sometimes referred to as the base.

And log base 10.

log of base a of b is the same thing as log base x, where x is arbitrary base of b over log base x over a.

So we know and these are all the same base we know that if we have log base a of b plus log base a of c that this is the same thing as log base a of bc.

Is equal to the log base x of b divided by the log base x of a.

Because log base x of a over log base x of a is equal to 1.

Use the change of base formula to find log base 5 of 100, to the nearest thousandth.

let's flip the base.

And that's essentially 0,0.

From there, we dove in.

Heptane, this is kind of the core.

We could have said, well, gee, this is the same base.

So logarithm with the same base.

That this is the same thing as the log base 10 of 3, divided by the log base 10 of 7.

Log base 5 twenty five to the x over y to this property means that its the same thing as log base 5 to the twenty five to the x power minus log base 5 of y

So let's see what this is. three times log base what's log base two of eight?

Let's look at this base.

You just have to pick the same base.

We have the exact same base, x.

Log base 3 of 27x.

I think we all already know that.

So you generally need to change your base.

log base 10 of x.

Is equal to log base x of b.

We've proven the change of the base formula.

This way of passing, they must be ahead of us.

We could say that's the same thing as log base ten of three hundred and fifty seven divided by log base ten of seventeen.

let me write it this way actually b times log base a of c this is equal to log base a of c to the b th power.

So you get c is equal to and I'll stick to the color so it's log base x of b over log base x of a.

And this is what c was, c was logarithm base a of b. ... is equal to log base a of b.

We're taking the base to the exponent of 3.