How do you change numbers with other bases to base ten?

Question

How do you change numbers with other bases to base ten?

Answer 1

for logarithims? theres a change of base equation but im not sure what it is sorry. maybe you could look it up.

Answer 2

Changing other bases to base 10

Look at each digit separately from right to left and multiply out according to what that position represents, then add the products.

For example,

21643 in base 7:

The 3 is the number of ones, or the number of 7^0s in the number: 3*(7^0)=3

The 4 is the number of 7s: 4*(7^1)=28

The 6 is the number of 7^2s: 6*(7^2)=6*49=294

The 1 is the number of 7^3s: 1*(7^3)=343

The 2 is the number of 7^4s: 2*(7^4)=16807

Add them up: 3+28+294+343+16807: 17475

17475 decimal equals 21643 in base 7

Another example:

DEA4 in hex (base 12):

4 is the number of ones: 4*(12^0)=4

A is the number of 12s: 11*(12^1)=132

E is the number of 12^2s: 15*(12^2)=2160

D is the number of 12^3s: 14*(12^3)=24192

Add them up.  4+132+2160+24192=26488

26488 decimal equals DEA4 in base 12

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