I am supposed to write each logarithmic expression as a single logarithm. I have logbase3of13 + logbase3of3 and my answer is logbase3of39. Can I simplify that any further?

also logbase3 of 3 is 1
1+ log3 13 is another answer, simpler, to me.

oh, okay, so it would make more sense to just simplify one side. thanks

oh, okay, so it would make more sense to just simplify one side. thanks

Yes, you are correct. The expression logbase3of13 + logbase3of3 can be simplified further.

To simplify the expression, we can use the logarithmic property that states log base a of m + log base a of n equals log base a of (m * n).

Using this property, we can simplify logbase3of13 + logbase3of3 as follows:

logbase3of13 + logbase3of3 = logbase3of(13 * 3)

The product of 13 and 3 is 39, so we can simplify further to:

logbase3of(13 * 3) = logbase3of39

Therefore, the simplified expression is logbase3of39.

However, you also mentioned that logbase3 of 3 is 1. In that case, we can simplify the expression further:

logbase3of13 + logbase3of3 = 1 + logbase3of13

So an alternative simplified expression is 1 + logbase3of13. Both logbase3of39 and 1 + logbase3of13 are correct simplifications, and which one you choose to use depends on your preference or specific requirements for the problem.

I hope this explanation helps! Let me know if you have any further questions.