Product Rule of Logarithms - Problem 1

Using the product rule of logarithms; so behind me I have a log where we are multiplying two things inside of the logarithms. 64 x is actually the same thing as 64 times x. So whenever we are multiplying inside the log we can break this up into addition of two logs.

The base remains the same, so what we end up with is log base 8 of one item so it's 64 for the first plus the log base 8 of the other item in this case x. So now using some properties of logs we can actually simplify one of this.

Log base 8 of 64 is saying what power of 8 will give us 64 which we know to be 2. So this whole term turns into 2 and we are left with the log base 8 of x on the outside. So using the product rule to write this as two different logarithms if we are going to hear this is using the term expand so you'll say expand this and you’d write it as two different logs.