Simplifying logarithms

Hello Helena,

If I correctly understood the equation, this is the best way (for me) to solve this problem.

I hope this helps. ^u^

Hi Shadow.

This helps a lot. I would never have thought of doing this.I am getting really confused about the exponents and how they can be manipulated.

I did this but am still not sure if it is correct.

I just highlighted some parts of the above to show where each part comes from. Is my reasoning correct?

Sorry to be a nuisance but this is one of the things which confuses me. Which one is correct. Is there an issue with my lack of brackets()?

Hello Helena,

I am happy that the first one helped you.  As for the log base 6 of 6 issue, this image might help you understand.

And yes, defining the brackets are really important.  Either you are squaring just the argument or the whole logarithm; both will give you different answers.

I tried to do the problem again in a different way and turned a bit more complicated than I thought it would be.  I do not know if this will help you, but it may show you the important role the brackets play.

P.S. I highly recommend NOT doing this way. 

Let me know if you are still confused or need help with anything else.

No, this is perfect. It shows me that it can be solved in different ways. The brackets thing was really an issue for me and is somewhat less confusing now.

I ended up solving the same problem in loads of different and often complex ways as you showed above but I think the exercise of doing so really helped me understand how logarithms work.

Thank you very much for taking the time to help me. You’re a star!

No problem.  Let me know if you need help with anything else.