What is the answer to (81^{3n+2})/(243^{-n)}=3^4 ?

The answer to (81^{3n+2})/(243^{-n)}=3^4 is n=-4/17

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(81^{3n+2})/(243^{-n)}=3^4

\frac{8 1 ^{3 n + 2}}{24 3 ^{- n}} = 3^{4}

n = - \frac{4}{17}

Decimal Notation

n = - 0.23529 \dots

Solution steps

\frac{8 1 ^{3 n + 2}}{24 3 ^{- n}} = 3^{4}

Apply exponent rules

4 (3 n + 2) + 5 n = 4

Solve

4 (3 n + 2) + 5 n = 4 : n = - \frac{4}{17}

n = - \frac{4}{17}

Verify Solutions:

n = - \frac{4}{17}

True

The solution is

n = - \frac{4}{17}

12 e^{2 x} = 200

2^{x} \times 3^{x} = 81

- x^{2} e^{- x} + 2 x e^{- x} = 0

2^{\frac{x}{2}} + 2^{x} = 6

7^{3 x + 1} = e^{x}

What is the answer to (81^{3n+2})/(243^{-n)}=3^4 ?
The answer to (81^{3n+2})/(243^{-n)}=3^4 is n=-4/17
Solve for n: (81^{3n+2})/(243^{-n)}=3^4
The solution is n=-4/17