Thank you for the opportunity to help you with your question!

So your expression, , is read as "base 3 logarithm of 27" we should be thinking of it as "the exponent for 3 that results in  So your problem is to figure out what power of 3 results in . If you know that  and if you're really good with exponents you will already know the answer. If you don't know the answer yet, then try to express  as a power of 3. Well, we can start by writing the 27 as a power of 3:


But what about the square root? Square roots are powers of 1/2. IOW, . So we can rewrite our square root as an exponent of 1/2:

The rule for exponents when raising a power to a power is to multiply the exponents:

We can now see what exponent on 3 results in ! An exponent of 3/2 on a 3 results in . So