Find the value of x for which \(32_{four} = 22_x\)
Answer Details
In this question, we are asked to find the value of x for which \(32_{four} = 22_x\).
We know that \(32_{four}\) means 3 fours plus 2 ones, which is equal to 14 in the decimal system.
So, we have:
$$14_{10} = 2\times x^1 + 2\times x^0 = 2x+2$$
Now we can solve for x:
$$14_{10} = 2x+2$$
$$12_{10} = 2x$$
$$x = 6_{10}$$
Therefore, \(32_{four} = 22_6\) and the value of x is 6.