Determine the base of the numbers in each case for the following operations to be correct: (a) 14/2 = 5
Question
Determine the base of the numbers in each case for the following operations to be correct:
(a) 14/2 = 5
Solution
To solve this problem, we need to find a base (n) for which the operation 14/2 = 5 is correct.
Step 1: Convert the numbers to base 10 The number 14 in base n is 1*n + 4 = 14 in base 10 The number 2 in base n is 2 in base 10 The number 5 in base n is 5 in base 10
Step 2: Set up the equation We know that 14/2 = 5, so we can set up the equation (1*n + 4)/2 = 5
Step 3: Solve for n Solving the equation gives us n = 6
So, the base of the numbers in this case is 6.
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