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2 years ago

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

Mathematics

1 answer:

Troyanec [42]2 years ago

6 0

9514 1404 393

Answer:

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

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bazaltina [42]

Answer:

$\Huge \boxed{p>11}$

Step-by-step explanation:

First, subtract by 7 both sides of equation.

$\displaystyle 12p+7-7>139-7$

Solve.

$\displaystyle 139-7=132$

$12p>132$

Then, divide by 12 both sides of equation.

$\displaystyle \frac{12p}{12}=\frac{132}{12}$

Solve to find the answer.

$\displaystyle 132\div12=11$

$\huge \boxed{p>11}$ , which is our answer.

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

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