Algebra

[rigid briar]

How to find y?

36!=x×3^(y) then what's the value of y?

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[fathom field]

do you know what factorials and powers are

[rigid briar]

Algebra

[rigid briar]

No

The question is 36!=x×3^(y) then what's the value of y

[fathom field]

36! means 36x35x34x33...x2x1.

[rigid briar]

Yeah

[fathom field]

3^y means 3x3x3 y times

[rigid briar]

x=3^(y)/36!

[rigid briar]

Yes

[timber totem]

what is x meant to be

y can be anything since x can be anything

[rigid briar]

Idk that's the question

[fathom field]

y is dependent on x

i think we have to find the relation between the two

[timber totem]

yup

i thought this was just the number of 3 powers but it clearly isnt it

[timber totem]

is there more context in the question??? or else its just plain unsolvable

or rather what do they want you to do

[fathom field]

can't we just say y root(36!) = 3x

[rigid briar]

No that's the question only

[rigid briar]

Find the y

[timber totem]

just isolate y then...?

i guess thats like the only thing you can do

[rigid briar]

So I can't get the value?

[timber totem]

nope

becasue you have two varaibles and one equation

[fathom field]

x is dependent on y

y is dependent on x

[rigid briar]

Yes

[fathom field]

tell us what x is and we can find y

[rigid briar]

Can we make 36! into 3^(something )?

[timber totem]

well yea but youd also have soemthing else

[rigid briar]

That's the question

[timber totem]

and that doesnt force x to be the other thing

we can transfer any power of y over to x

[fathom field]

we can't find out y in that case

[timber totem]

or we could do real solutions lmao

we could set y= 8.803176081730516 and a value of x exists 💀

[fathom field]

i guess we have to find the relation

[fathom field]

exactly

[rigid briar]

Then maybe that's the wrong question. Thanks @fathom field @timber totem for helping me

[fathom sand]

@rigid briar has given 1 rep to @fathom field @timber totem

[timber totem]

yw! gl with the question lol

[fathom field]

this is like giving a 5 year old "if x = 1/0 find x" 💀

[delicate pendant]

I think the question asks for the number of 3's factors in 36!

[timber totem]

but theres an x

and it doesnt specify x is anything in particular

[rigid briar]

Yes yes u got it right. If we can find that then y= (of that number)

[timber totem]

or that y needs to be an integer

[delicate pendant]

yea I think both x and y must be integers

[timber totem]

still like a ton of solutions

[fathom field]

graph

[delicate pendant]

how so?
wouldn't then we can find the value of y by prime factorising each of the factors from 1 to 36 and sum up all the exponents of 3's?

[timber totem]

the graph clearly says im wrong whar

[sharp raptor]

and 3 is not a factor of x, presumably

[timber totem]

like if we have 6! we can have y=-0, 1, 2
so 6!=3^2 * 80
or 3^1 * 240
3^0 * 720

[timber totem]

yea that would make sense

[rigid briar]

Well the value of y is 17

But how?

Someone told me this answer

[timber totem]

are we assuming x/3 is not an integer and x,y are integers

yea just assume that

i assume swindle is cooking up the soln

[fathom field]

2880539393386867704882790400000000 = x

find the relation between x and y

[delicate pendant]

3 = 3¹
6 = 2×3¹
9 = 3²
12 = 2²×3¹
15 = 3¹×5
18 = 2×3²
21 = 3¹×7
24 = 2³×3¹
27 = 3³
30 = 2×3¹×5
33 = 3¹×11
36 = 2²×3²
sum up all the exponents of 3's
1+1+2+1+1+2+1+1+3+1+1+2 = 17

[timber totem]

i usually do this by like
number of 3 factors: 36/3 = 12
number of 9 factors: 36/9 = 4
number of 27 factors: floor(36/27) = 1
number of 81 factors: none

and theres an interesting pattern here which is that

for n! and i want to find the number of a prime p to the k

[rigid briar]

Yes yes that's the solution! Thank youuuuu sooooo much swindleee. I understood it now

[delicate pendant]

urwelcome

[fathom sand]

@rigid briar has given 1 rep to @delicate pendant

[timber totem]

first do floor n/p + floor n/p^2 + floor n/p^3
or in this case 36/3 = 12 then divide by 3 to get 4 then divide by 3 and floor it to get 1

its strange why this works but ok

[delicate pendant]

it's cuz 36/9 = (36/3)/3 = 12/3
and 12 is the result of the previous
and so on

[timber totem]

yea

probably could prove it

[graceful kestrel]

Legendre's formula

[dense moon]

$36! = 3^{\log_3(36!)}$

[vivid cobalt]

mark4slr