iluvvyyhu 3 years ago Help with logs?Cant use a calculator?:( Evaluate, without using a calculator 5^(-2)

1. iluvvyyhu

Oh wait i put the wrong one sowwy :( $\log _{6}1$

2. ludwig457

log(a)y = a^y

3. iluvvyyhu

im a little confused.....would it be $6^{1}$ than?

4. ludwig457

yes :)

5. iluvvyyhu

ohh okay thankyou(: um may you help me with another one? Its a fraction?

6. ludwig457

yesm

7. iluvvyyhu

thankyou!(: okay here it is$\log _{6}\frac{ 1 }{ \sqrt[5]{36}}$ sorry it took a while to type it lol

8. ludwig457

i did the first one wrong it should be log(a)x = y and a^y =x

9. iluvvyyhu

ohh... okay im confused now :(

10. ludwig457

the second one is a little out of my league lol you should open a new question with that second part!

11. iluvvyyhu

lol alright but may you explain the first one pleaseee?(: <3

12. ludwig457

so log(a)x is the exponent to which the base a must be raised to give x

13. ludwig457

so to raise 6 by a power of zero will give an output of 1. any number raised to zero will give 1

14. ludwig457

x^0=1

15. ludwig457

2^0=1 and so on

16. iluvvyyhu

so.... okay im not 100% sure but would the answer be 1?

17. iluvvyyhu

Oh and another question (sorry lol) so do you always raise the little number by 0?

18. ludwig457

log(6)1=0 6^0=1

19. ludwig457

nope you 'exponentiate' the little number

20. ludwig457

log(6)1=0 since 6^0=1

21. iluvvyyhu

okay okay...what does exponentiate mean im sorry for all these questions

22. ludwig457

The act of raising a quantity to a power :)

23. iluvvyyhu

okay(: but im still confused :'(

24. ludwig457

they confuse me too hehe

25. ludwig457

log(a)x = y <=> a^y = x

26. ludwig457

just remember that a is your base, the base will always be the same for any log

27. ludwig457

any number raised to a power like a^x, a will be your base

28. ludwig457

imm off gluck

29. iluvvyyhu

alright:/ thanks though <3