Logarithm question

1. Nov 12, 2013

chemistry1

Hi, quick question.

Is there a difference in notation when I say :

(log8(x))^2

and

log8(x)^2

Is it different or the same ??? Thank you !

2. Nov 12, 2013

goldust

I would say they mean the same thing. log8(x^2) would be different. To me, at least, log8(x)^2 means squaring log8(x). Hope that helps!

Last edited: Nov 12, 2013
3. Nov 12, 2013

chemistry1

Well, I thought that saying log8(x)*log8(x) would be different than log8(x)^2

Ill keep waiting

Thank you

4. Nov 12, 2013

goldust

You can try it out on a calculator and see if there is any difference between (log8(x))^2 and log8(x)^2.

http://web2.0calc.com/

5. Nov 12, 2013

chemistry1

Yeah, it seems to say that it's the samething. COuld you try it on this one, I have doubts :https://www.mathway.com/

Thank you

6. Nov 12, 2013

Staff: Mentor

The first one is clear, but the second one is ambiguous. It could be interpreted as either (log8(x))2, or as log8(x2).

Parentheses should be used to make your meaning clear.

7. Nov 12, 2013

chemistry1

But with the first one could I say something like : 2*(log8(x)) ??? ty

8. Nov 12, 2013

goldust

I don't see why not. What's in brackets is considered a single entity.

9. Nov 12, 2013

Staff: Mentor

(log8(x))2 ≠ 2*log8(x) !! That's not how the log properties work.
loga(x2) = 2 loga(x). This isn't what you have in the first example.

See above.

10. Nov 12, 2013

goldust

Of course. :tongue:

Last edited: Nov 12, 2013
11. Nov 12, 2013

economicsnerd

As Mark44 said, just use parentheses to make things unambiguous.
- $(\log_8 x)^2$ means one thing.
- $\log_8 (x^2)$ means another thing (which happens to be the same thing that $2\log_8 x$ means).
- Nobody is stopping you from writing $\log_8(x)^2$, but I wouldn't write it, because it's not crystal clear what it means.

12. Nov 12, 2013

chemistry1

Ok, but what is the meaning of : (log8(x))^2

is it (log8(x))(log8(x)) ???

13. Nov 12, 2013

goldust

Yes, this is clear.

14. Nov 12, 2013

chemistry1

And how would you simplify it ??

log8 x^log8(x)

Is this valid ???

15. Nov 12, 2013

goldust

To me, this is the same as log8 (x^log8(x)), because you can only have a single input with the function log8.

Last edited: Nov 12, 2013
16. Nov 12, 2013

chemistry1

Look, here's the reason why I'm asking the question :

(log8(x))^2+2(log(x))+1=0

I'm not able of finding a way to solve this. The closest answer I got was 1/64. Can somebody help me ???

17. Nov 12, 2013

Staff: Mentor

Yes.

Not if you mean (log8(x))2

18. Nov 12, 2013

Staff: Mentor

Did you omit the base in the second term? Should it be log8(x)?

If so, your equation is quadratic in form. If you let u = log8(x), then the equation can be written as x2 + 2x + 1 = 0, which can be factored.

19. Nov 12, 2013

chemistry1

Ahh..... WEll... Thank you !

20. Nov 12, 2013

chemistry1

AH yes, I forgot it ! What do you mean by u= ... ???