Dealing With Logs: 3log(AB), is this equal to log(AB^3), log(AB)^3, log ((AB)^3) ?

[Ted_Grendy]

Hi All

I was hoping someone could help with the following question about logs.

I have 3log(AB), is this equal to:-

1) log(AB^3)
2) log(AB)^3
3) log ((AB)^3)

Thanks

 

[Harry_the_cat]

What do you think and why?
Do you know the log rule involving powers?

 

[Steven G]

Hi All

I was hoping someone could help with the following question about logs.

I have 3log(AB), is this equal to:-

1) log(AB^3)
2) log(AB)^3
3) log ((AB)^3)

Thanks

Hint 1: 5log(t) = log (t⁵). Hint 2: (uv)⁵ = u⁵v⁵

 

[Dr.Peterson]

I was hoping someone could help with the following question about logs.

I have 3log(AB), is this equal to:-

1) log(AB^3)
2) log(AB)^3
3) log ((AB)^3)

I was hoping you would tell us what you are thinking, so we could be sure what help you need.

One possibility is that you are unsure of the order of operations.

In the first expression, only B is being cubed.

In the second, we are taking the log of AB, since that is what is in parentheses and is therefore the argument of the function; and then cubing the result. But this is sufficiently ambiguous that I would avoid writing it.

In the third, the ambiguity has been removed: we are clearly cubing AB, then taking the log of that.

Which of these means what it has to mean?