Answer:
To find the value of base "x" given that 331 base x is equal to 61 base ten, you can set up an equation and solve for "x."
In base x, the number 331 represents:
3*x^2 + 3*x + 1
And in base ten, the number 61 is itself.
So, we can write the equation:
3*x^2 + 3*x + 1 = 61
Now, subtract 61 from both sides of the equation:
3*x^2 + 3*x + 1 - 61 = 0
Simplify the equation:
3*x^2 + 3*x - 60 = 0
Now, you can factor the equation:
3(x^2 + x - 20) = 0
Next, solve for x by factoring the quadratic equation:
(x + 5)(x - 4) = 0
Now, you have two possible solutions:
1. x + 5 = 0, which gives x = -5
2. x - 4 = 0, which gives x = 4
However, in base systems, we typically use positive integer values for the base. So, the value of base "x" in this case is 4, as it cannot be negative.
Explanation:
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