If 32_x = 23_{10}, find the value of the base x. — JAMB UTME

If $32_x = 23_{10}$ , find the value of the base $x$ .

Answer: 7

Expanding the number

32_x

into base 10 gives

3 \times x + 2 = 3x + 2

. Setting

3x + 2 = 23

leads to

3x = 21

, giving

x = 7

Expand

32_x

in terms of powers of

x

3x + 2

In base

x

, the rightmost digit has a weight of

x^0 = 1

and the next digit to the left has a weight of

x^1 = x

Equate the expanded form to the given base 10 value and solve for

x

x = 7

Setting

3x + 2 = 23

gives

3x = 21

, which yields

x = 7

upon dividing by 3.

Expansion and conversion from Base x to Base 10

Estimated Time:45s

Question