Solve the problem, 132 base (x)=72 base ten

Answer 1

To solve for x, we need to convert the number 72 from base 10 to base x.

Let's start by finding the largest power of x that is less than or equal to 72.
For base 1, 1^6 = 1, 1^7 = 1, and 1^8 = 1. So, x must be greater than 1.

For base 2, 2^6 = 64, 2^7 = 128 (which is greater than 72), and 2^5 = 32.
Since 2^6 is greater than 72, we can conclude that x must be less than 2.

For base 3, 3^4 = 81 (which is greater than 72), 3^3 = 27, and 3^2 = 9.
Since 3^3 is less than 72, we can eliminate base 1 and 2.
Therefore, x must be 3.

Now, let's convert 72 base 10 to base 3.

To do this, we need to find the largest power of 3 that is less than or equal to 72.
3^3 = 27, 3^4 = 81 (which is greater than 72), and 3^2 = 9.
Since 3^3 is the largest power of 3 less than 72, let's proceed with dividing 72 by 27.

72 divided by 27 is 2 with a remainder of 18.

Now, we divide the remainder (18) by the next lower power of 3, which is 3^2.

18 divided by 9 is 2 with a remainder of 0.

Lastly, we divide the remainder (0) by the lowest power of 3, which is 3^1.

0 divided by 3 is 0 with no remainder.

Therefore, the decimal number 72 base 10 is equivalent to 200 base 3.