Power Rule of Logarithms - Problem 1

Using the power rule to rewrite logarithms. So behind me I have a series of problems and what we are basically what we are going to do is use the power rule to rewrite them. And what the power rule is saying is if you have a term in your log with an exponent you can take the exponent and bring it outside.

With this 4 you can bring out front, 4 log base 7, 3 we can’t simplify log base 7, 3 so is really how we can do it. Log base 4 1 over x to the fifth so this one we have to go back to some negative exponents and we write we can rewrite 1 over x to the fifth as log base 4, x to the negative fifth, and now we can bring that negative out to the front, -5 log base 4, x.

Last one I’m going to look at is log base 8 of 8 to the fifth. You can bring the 5 down in front, end up with 5 times log base 8 of 8. Log base 8 of 8 we actually know what that is. That’s just going to be 1. This is 1, and what we are left with is just 5.

That’s one of the property of logs, is if we have log base b of b to the x we could bring this x around and we know that log base b of b is just going to be 1, so this is just going to leave us with x.

So using the power rule to move around some exponents.