# Change of base

#### pickslides

##### Member
Re: Find the missing base 100101 two = 31 ______

Firstly, what is $100101_2$ in decimal?

#### vivalajuicy

##### New member
Re: Find the missing base 100101 two = 31 ______

Firstly, what is $100101_2$ in decimal?
a whole number

#### pickslides

##### Member
Re: Find the missing base 100101 two = 31 ______

It is, but more accurately $2^0\times 1+2^1\times 0+2^2\times 1+2^3\times 0+2^4\times 0+2^5\times 1 = \dots$

Make that result equal to $31_x = x^0\times 1+x^1\times 3$ and solve for $x$

#### vivalajuicy

##### New member
Re: Find the missing base 100101 two = 31 ______

It is, but more accurately $2^0\times 1+2^1\times 0+2^2\times 1+2^3\times 0+2^4\times 0+2^5\times 1 = \dots$

Make that result equal to $31_x = x^0\times 1+x^1\times 3$ and solve for $x$
thank you!!