[SOUND] We're going to learn about The Change of Base Formula for Logarithms

here. [SOUND] How would we compute log base 3

of 5? Now remember, that log base a of x = y, if and only if a to the y = x.

For example, log base 3 of 9 = 2, since 3^2=9.

But, looking at our problem over here, do we know a power that we can raise 3 too,

to get 5? We don't. And so, we'd like to use our calculator,

but how? Most calculators, only have two log buttons.

They have, log, which means log base 10, then they have l-n, which means log base

e. But they don't have a log base 3 button.

So how are we going to compute log base 3 of 5? Well, we can use a change of base

formula for log. x.

Which states, that we can change our base from a to c, as long as we divide by the

log of our old base. So let's apply that here, with a=3.

b=5, And, we can use c=10, because we have that button on our calculator.

Now, we could've also used c=e, because we have that button as well.

But, let's use base 10. That is, log base 3 of 5, is equal to log

base 10, of 5, divided by log base 10 of 3.

And we don't normally write the base 10, so this is log 5 divided by Log 3, which

when we plug into our calculator, we get 1.4649 and so on.

Now if we would have used c = e, we would have arrived at the same answer.

So this change of base formula for logs is very handy, when we need to use the

calculator to compute a logarithm. Thank you and we'll see you next time.

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