Find n if 142n=47(10)

Answer 1

If your question is:

142 base n = 47 base ten

142ₙ = 47₁₀

then

47₁₀ = 47

142ₙ = ( 1 • n² ) + ( 4 • n¹ ) + ( 2 • n⁰ )

142ₙ = 47

( 1 • n² ) + ( 4 • n¹ ) + ( 2 • n⁰ ) = 47

n² + 4 n + 2 • 1 = 47

n² + 4 n + 2 = 47

Subtract 47 to both sides

n² + 4 n - 45 = 0

The solutions are:

n = - 9 and n = 5

A negative number cannot be the base of a number.

- 9 cannot be the base of a number.

So n = 5

142₅ = 47₁₀