1. Given that (27 ^ (n + 3))/(81 ^ (p - 1)) = 3 , express p in terms of h.​

9514 1404 393

  p = 3/4n +3

Step-by-step explanation:

Expressing the given equation in terms of powers of 3, we have ...

  (27^(n+3))/(81^(p-1)) = 3

  (3^3)^(n+3)/(3^4)^(p-1) = 3^1 . . . . as powers of 3

  3(n +3) -4(p -1) = 1 . . . . . . . . . . . . log base 3 (or, equate exponents)

  3n +9 -4p +4 = 1 . . . . . . . . . . . . . eliminate parentheses

  3n +12 = 4p . . . . . . . . . . . . . . . . add 4p -1

  p = 3/4n +3 . . . . . . . . . . divide by 4

mx+89b(-98)nb

step-by-step explanation: