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? asked in Science & MathematicsMathematics · 2 days ago

3^x × 9^4 = 3^n Find n in terms of x.?

6 Answers

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  • Pinkgreen
    Lv 7
    19 hours ago

    (3^x)(9^4)=3^n

    =>

    (3^x)(3^8)=3^n

    =>

    3^(x+8)=3^n

    =>

    x+8=n

    (by comparison)

  • Krishnamurthy
    Lv 7
    2 days ago

    3^x × 9^4 = 3^n

    3^x × 3^8 = 3^n

    n = 8 + x

  • la console
    Lv 7
    2 days ago

    3^(x) * 9^(4) = 3^(n)

    3^(x) * [3^(2)]^(4) = 3^(n)

    3^(x) * 3^(8) = 3^(n)

    3^(x + 8) = 3^(n)

    x + 8 = n

  • Jeff Aaron
    Lv 7
    2 days ago

    (3^x)(9^4) = 3^n

    6561(3^x) = 3^n

    6561 = (3^n)/(3^x)

    3^(n - x) = 6561

    n - x = (ln(6561) + 2*i*pi*m) / ln(3), for any integer m

    n - x = 8 + ((2*i*pi*m) / ln(3)), for any integer m

    n = x + 8 + ((2*i*pi*m) / ln(3)), for any integer m

    n =~ x + 8 + 5.7192017347602545393042808406673im, for any integer m

    If n and x are real numbers, then m = 0, so n = x + 8

    Source(s): https://www.wolframalpha.com/input/?i=3%5Ex+%C3%97...
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  • Ash
    Lv 7
    2 days ago

    3 ͯ  x 9⁴ = 3ⁿ

    3 ͯ x (3²)⁴ = 3ⁿ

    3 ͯ x 3⁸ = 3ⁿ

    3⁽ ͯ ⁺⁸⁾ = 3ⁿ

    x+8 = n

  • lenpol7
    Lv 7
    2 days ago

    Remember 9 = 3^2 

    Apply the rules of indices. 

    3^x X (3^2)^4 = 3^n 

    3^x X 3^8 = 3^n 

    3^(x + 8) =3^n

    Dropping the coefficient of '3' 

    n = x + 8  

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