Question

Write \(log_6~5\) as a logarithm of base 4.

Answer 1

@sleepyjess Any help? :/

Answer 2

uuuuuhhhhh give me a min

Answer 3

Omg thanks! :D

Answer 4

A its 100% A

Answer 5

Do you know the change of base formula

Answer 6

@blueSurrency wow you got it right with no options! jk

@sleepyjess no I don't :(

Answer 7

darn, that gives an actual numerical value though such as 1.48q4r734rq387...

Answer 8

I know what it isuld I use it here?

Answer 9

how would*

Answer 10

Oh, nevermind, if you don't fully complete it, it just changes the base, ok

Answer 11

Okay i answered the wrong question so love the sarcasm tho!

Answer 12

its (log4)5/(log4)6

Answer 13

change of base formula:
\(\sf log_bx\\\dfrac{log_dx}{log_db}\)

Answer 14

d is the new base

Answer 15

Please don't give direct answers @blueSurrency

Answer 16

Thanks for the tip

Answer 17

I see

Answer 18

you wont like this but i guess below is the simplest method to change base w/o using change of base formula directly : \[\large \log_{\color{Red}{6}}~\color{green}{5}= \log_{\color{red}{4^{\log_46}}}~\color{green}{4^{\log_45}}\]
\[\large \color{green}{4^{\log_45}} = \left({\color{red}{4^{\log_46}}}\right)^?\]

Answer 19

O_O I have never seen that before...

Answer 20

Jess, it's because ganeshie8 gots all those smart brains ;D

Answer 21

he does have all those smart brains...

Answer 22

<3 idk why but your name reminds me of the most smartest person on openstudy @YanaSidlinskiy

Answer 23

@ganeshie8 O_O How did you do that????

Answer 24

I think we are pretty much all confuzzled about @ganeshie8 's method...

Answer 25

Bayana's_republic

Answer 26

\[\text{ \let } u=\log_6(5) \\ \text{ \to get rid of the base 6 do } 6^u=6^{\log_6(5)} \\ \text{ so we have } 6^u=5 \\ \text{ now we can chose \to solve for u using base 4 instead } \\ \log_4(6^u)=\log_4(5) \\ u \log_4(6)=\log_4(5) \\ \text{ solve for u }\]

Answer 27

that is another way to look at it

Answer 28

LOL, @ganeshie8

Answer 29

ok I have no what you did... but from what I do know is that with what you said \(log_4~(6^u)\) is the same as \(log_4~(5)\) Right?

Answer 30

that looks neat :)

Answer 31

sleepyjess's formula is what we use to get the work done @Joel_the_boss :

\[\large \sf log_{\color{Red}{b}} \color{green}{x }= \dfrac{log_d \color{green}{x}}{log_d\color{red}{b}}\]

Answer 32

\[\large \sf log_{\color{Red}{6}} \color{green}{5 }= \dfrac{log_4 \color{green}{5}}{log_4\color{red}{6}}\]

thats it! now the right side terms are in base 4 ^

Answer 33

So, if I am reading this right, I used the easy formula and you just showed it differently?

Answer 34

What? That's all? That's easy!!! @ganeshie8 and @sleepyjess You guys saved me hours of struggle...... Wait math cant be this easy... Whats the catch?

Answer 35

thats right, formlas are meant to be easy and make life simple :)

Answer 36

*math life ofc

Answer 37

catch? there is no catch... as @ganeshie8 said, formulas are meant to make life simple

Answer 38

I would have never gotten through this module in pre-calc if it weren't for formulas for law of sines and law of cosines...

Answer 39

O_O I love you guys, @ganeshie8 Why arn't you teaching? You should be my teacher!!

Answer 40

*Cough* He's teaching me, not you. <3

Answer 41

hahahah hes got a more prestigious job than teaching
And .... Hes one of the the most sought after teachers on OS ;)

Answer 42

Uu....^ He still teaches me. And I know he enjoys it:P

Answer 43

If I was a principal I would pay him twice as much, and give him his own parking spot. xDD Thanks again for the help @ganeshie8 before today a log was a piece of wood. And might wanna check the newest post for questions. :P