Question

Can someone please help me with BASES! I need to find a base that makes this statement true: 135b+444b=601b. Where do I even start?! :(

Answer 1

would making them all base 10 work?

Answer 2

b represent the base

Answer 3

perhaps write the expression as log base 135 (x) + log base 444 (x) = log base 601 (x) . I wrote x so that they are all related , then try changing the base to 10 , from there try some log manipulation . I would not know how else to appraoch this problem

Answer 4

i dont understand the process though, like once i do what you suggested, how do i convert them to base 10?

Answer 5

log base 135 (x) = log base 10 (x) / log base 10 (135) That is what I found on google . but you might want to double check. this approach may be the incorrect one . nonethe less its a thought

Answer 6

im not familiar with bases at all but ill try! thank you!

Answer 7

@ganeshie8 can you please help me with this problem?

Answer 8

applying the change in base that would mean you would also have to find a commonality that between the 136 , 444 , and 601 . In base 10 I dont think those values are acceptable , you might have try try a different base

Answer 9

135
444
-----
601


look at the units place addition
5+4 = 11

Answer 10

\[(5+4)_b = (11)_b\]
\[ 9 = 1*b^1 + 1*b^0\]
\[ 9 = b+1\]
\[ 8 = b\]

Answer 11

so does that mean that base 8 makes the entire statement true?

Answer 12

Yes

Answer 13

how did you know to do that?

Answer 14

13 `5`
44 `4`
-----
60 `1`

Answer 15

Notice that adding the last digits is producing a carry :
`1`
13 `5`
44 `4`
-----
60 `1`

Answer 16

that means \((5+4)_b = (11)_b\)

did u get this far ?

Answer 17

so thats just (11)b=11b?

Answer 18

oh no! (9)b=(11)b?

Answer 19

in the next step we're changing everything to base 10

Answer 20

5+4 = 9 in base 10

Answer 21

\((5+4)_b = (11)_b\)

\((9)_{10} = 1\times b^1 + 1\times b^0\)

Answer 22

you must be knowing converting a different base number to base10 ?

Answer 23

i don't have much experience with bases :( thats what I'm trying to figure out

Answer 24

Lets start from scratch

Answer 25

so you're comfortable only with base10 ?

Answer 26

yes! i am barely learning base 10

Answer 27

the main reason humans use 10 symbols to count is because they have 10 fingers

Answer 28

makes sense! haha

Answer 29

An alien with only 5 fingers might feel comfortable using base5 instead :
\( (4 + 4)_{5} = (13)_5\)

Answer 30

lets see how the alien is getting 13 for that addition in base5

Answer 31

suppose we give the alien \(8\) stones and ask it to count :

Answer 32

so 1 set and 3 extra

Answer 33

it starts counting up to 5 using its 5 fingers and puts it aside and says it is one `five`: