Asked by ONWUAZOMBE IFUNANYA
Find n if 142n=47(10)
Answers
Answered by
Bosnian
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
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
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