# How do you combine #\log _ { 9} 36- \log _ { 3} 2+ \log _ { 0.5} 4#?

##### 1 Answer

#### Explanation:

So what the logarithm function is asking is, what is the exponent that the base needs to be raised to to obtain the value, ie

Means that

So what we have is that

Take logs of both sides:

Now use the exponent rule of logs, ie

Now we can simplify some of these. Let's start with a.

Since we're going to be using b as well it would be helpful if we could get a into a similar form...luckily we can! Using the addition rule of logs:

So:

That's us got a and b looking nice so now we turn our attention to c.

Therefore