Question

MEDAL <3 Log question: Evaluate with out calculator:

Answer 1

\[\log _{64}4= ?\]

Answer 2

Ik the answer is 1/3 but I don't know how or why

Answer 3

lets say y = log_64 (4)

what would you say 'undoes' the log? any thoughts?

Answer 4

So b raised to ___ =64?

Answer 5

Ik they're similar in some way I just don't see the connection :/

Answer 6

recall the log rule:

sounds like your thinking of the righ tthing

b^(log_b (x)) = x

so lets base 64 both sides to undo th elog_64

64^y = 4

now i spose the way i would attempt a solution is to see if 4 and 64 have any factors in common

Answer 7

uhhh ok let me write this :)

Answer 8

Ah yay, factoring -.-

Answer 9

what is 64/4?

Answer 10

16!

Answer 11

Omg wait 3 times 4 is 16

Answer 12

Is it like that for all of them?

Answer 13

No it's not I just checked on another problem -___- oh well

Answer 14

so:

4*16 = 64, or 4*4*4 = 64

lets cube both sides ....

\[(64^y)^3=(4)^3\]
\[(64^y)^3=(64)^1\]
now comes another rule:
\[\large (a^m)^n=a^{mn}\]
apply it
\[(64^{3y}=(64)^1\]
what can we determine now?

Answer 15

My brain would have never thought like that... Is there any tips you have because I would've never known 4*4*4=64?

Answer 16

when you hit a road block, think of ways to get past it.

i know that if this has any possible way of being 1/3 that both sides must have something in common. 64 and 4 would have to be related in some fashion. common factors seemed appropriate to me.

Answer 17

64^(3y) = 64^(1) if and only if ... 3y=1

what is y?

Answer 18

Ok ok let me process this! & give u a medal before I forget but plz wait D:

Answer 19

Uh, I'm not sure why 3y has to = 1?

Answer 20

OH I GET IT THE BASES ARE THE SAME!

Answer 21

summary
\[y=log_{64}(4)\]
\[64^y=64^{log_{64}(4)}\]
\[64^y=4\]
\[note:4^3=64~:~so~cube~it~all\]
\[(64^y)^3=(4)^3\]
\[rule:(a^m)^n=a^{mn}~:~use~it\]
\[64^{(3y)}=64^{(1)}\]
\[3y=1\]

Answer 22

yes, same bases :)

Answer 23

if we log_64 both sides the 64s clear out and we are left with 3t=1 if you want to include a step

Answer 24

Wow thank you, you didn't have to!!

Answer 25

youre welcome, and good luck ;)

Answer 26

Okay, so we just- OMG I get it thank you!!!!

Answer 27

Two questions, how long did it take you to get to 99?

Answer 28

i was at the top long before they started using number values .. so i was 99 when they started this new system by default.

Answer 29

Also um.... uhhh.. I forgot damn it. Oh well, thank you!

Answer 30

OH WAIT I REMEMBER: Is there a way to view all your past asked questions?

Answer 31

placement was based on fan counts when i started. then they applied silly titles, then a medal system was integrated, ive been pretty much just floating by at the top ....

Answer 32

Ok thanks got it haha! :D It would be cool if they gave scholarships for doing this!

Answer 33

hover your icon in the top right corner and go to your 'profile' page. questons asked and answered is an option after it loads.