x is defined as one more than the number of digits in the number x . For example , 1000 = 5. For what value of x wil x = x ?
To find the value of x where x = x, we need to substitute the given expression into the equation and solve for x.
The given condition is that x is defined as one more than the number of digits in the number x. Let's rewrite this condition as an equation:
x = 1 + the number of digits in x
To solve this equation, we can break it down into cases based on the number of digits in x.
Case 1: x has 1 digit
If x has 1 digit, then according to the equation, x = 1 + 1 = 2. However, x does not equal 2, so this case is not valid.
Case 2: x has 2 digits
If x has 2 digits, then according to the equation, x = 1 + 2 = 3. Again, x does not equal 3, so this case is not valid.
Case 3: x has 3 digits
If x has 3 digits, then according to the equation, x = 1 + 3 = 4. Once again, x does not equal 4, so this case is not valid.
Case 4: x has 4 digits
If x has 4 digits, then according to the equation, x = 1 + 4 = 5. In this case, x equals 5, which satisfies the condition x = x.
Therefore, the value of x where x = x is x = 5.