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Adding, multiplying and dividing in base 7

So I have these 4 questions about adding, multiplying and dividing in base 7, and I've been trying but I just get confused: 1) 5+15 2) 2 x 14 3) 33/15 4) 425 x 32 Please help me! :smile: (All the numbers are in base 7, and the answer need to be in base 7 too) Thank you
Reply 1
Avatar for Dingo749
Dingo749
9
Original post by Tris2807
So I have these 4 questions about adding, multiplying and dividing in base 7, and I've been trying but I just get confused: 1) 5+15 2) 2 x 14 3) 33/15 4) 425 x 32 Please help me! :smile: (All the numbers are in base 7, and the answer need to be in base 7 too) Thank you


log⁡75+log⁡715\log_7 5 + \log_7 15 If you mean like this then you should just use the laws of logs?

log⁡ax+log⁡ay=log⁡axy\log_a x + \log_a y = \log_a xy

log⁡ax−log⁡ay=log⁡a(xy)\log_a x - \log_a y = \log_a (\dfrac{x}{y})

log⁡axlog⁡ay=log⁡yx\dfrac{\log_a x}{\log_a y} = \log_y x

log⁡xk=klog⁡x\log x^k = k \log x
Reply 2
Avatar for TenOfThem
TenOfThem
18
Original post by Tris2807
So I have these 4 questions about adding, multiplying and dividing in base 7, and I've been trying but I just get confused: 1) 5+15 2) 2 x 14 3) 33/15 4) 425 x 32 Please help me! :smile: (All the numbers are in base 7, and the answer need to be in base 7 too) Thank you


Personally I would convert to decimal and the revert to base 7 but that is because I am lazy

Are you allowed to do that - if not - show some working
Reply 3
Avatar for davros
davros
16
Original post by Tris2807
So I have these 4 questions about adding, multiplying and dividing in base 7, and I've been trying but I just get confused: 1) 5+15 2) 2 x 14 3) 33/15 4) 425 x 32 Please help me! :smile: (All the numbers are in base 7, and the answer need to be in base 7 too) Thank you


I'll do the first one to get you started. It's exactly the same as the arithmetic you learnt in primary school but you must remember to "carry" when you get a total of 7 or more.

5 = 5 units
15 = 1 seven and 5 units
5 units+ 5 units = 10 units = 1 seven and 3 units
Therefore the total is 1 seven + 1 seven + 3 units = 2 sevens and 3 units.

Therefore 57+157=2375_7 + 15_7 = 23_7


Original post by Dingo749
log⁡75+log⁡715\log_7 5 + \log_7 15 If you mean like this then you should just use the laws of logs?

...


This is nothing to do with logs - it's arithmetic in a different number base!
Reply 4
Avatar for Dingo749
Dingo749
9
Original post by davros
I'll do the first one to get you started. It's exactly the same as the arithmetic you learnt in primary school but you must remember to "carry" when you get a total of 7 or more.

5 = 5 units
15 = 1 seven and 5 units
5 units+ 5 units = 10 units = 1 seven and 3 units
Therefore the total is 1 seven + 1 seven + 3 units = 2 sevens and 3 units.

Therefore 57+157=2375_7 + 15_7 = 23_7




This is nothing to do with logs - it's arithmetic in a different number base!


Ahhh misunderstood thought this was about logs :smile: My bad!
Reply 5
Avatar for ztibor
ztibor
10
Original post by Tris2807
So I have these 4 questions about adding, multiplying and dividing in base 7, and I've been trying but I just get confused: 1) 5+15 2) 2 x 14 3) 33/15 4) 425 x 32 Please help me! :smile: (All the numbers are in base 7, and the answer need to be in base 7 too) Thank you


For multiplication/division write down the switch table for multiplication

X
1x1=1 1x2=2 ....... 1x6=6
2x1=2 2x2=4 ...... 2x6=15
3x1=3 3x2=6 ........ 3x6=24
....
6x1=6 6x2=15 ..... 6x6=51

so 14 x 2
------
3 1

1 5 x 2
----
3 3

So 33/15=2

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