If 23x = 325, find the value of x

If 23_x = 32₅, find the value of x

Answer Details

To find the value of x, we need to determine what base value the number 23_x represents. We are told that 23_x is equal to 32₅. In other words, the value represented by 23_x is equal to the value represented by 32₅. We can convert 32₅ to base 10 to get: 32₅ = (3 x 5¹) + (2 x 5⁰) = 15 + 2 = 17 So, we have: 23_x = 17 To find the value of x, we need to determine what base value raised to what power is equal to 17. We can do this by trying different values of x. If x is 2, then 23₂ = (2 x 2¹) + (3 x 2⁰) = 4 + 3 = 7 If x is 3, then 23₃ = (2 x 3¹) + (3 x 3⁰) = 6 + 3 = 9 If x is 4, then 23₄ = (2 x 4¹) + (3 x 4⁰) = 8 + 3 = 11 If x is 5, then 23₅ = (2 x 5¹) + (3 x 5⁰) = 10 + 3 = 13 If x is 6, then 23₆ = (2 x 6¹) + (3 x 6⁰) = 12 + 3 = 15 If x is 7, then 23₇ = (2 x 7¹) + (3 x 7⁰) = 14 + 3 = 17 So, we have found that if x is 7, then 23_x = 17, which matches the value of 32₅. Therefore, the value of x is 7. Answer: 7