What is the answer to 4^{-3n-2}*8=16^{3n-2} ?

The answer to 4^{-3n-2}*8=16^{3n-2} is n= 7/18

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4^{-3n-2}*8=16^{3n-2}

4^{- 3 n - 2} \cdot 8 = 1 6^{3 n - 2}

n = \frac{7}{18}

Decimal Notation

n = 0.38888 \dots

Solution steps

4^{- 3 n - 2} \cdot 8 = 1 6^{3 n - 2}

Apply exponent rules

(- 3 n - 2) ln (4) + ln (8) = 2 (3 n - 2) ln (4)

Solve

(- 3 n - 2) ln (4) + ln (8) = 2 (3 n - 2) ln (4) : n = \frac{7}{18}

n = \frac{7}{18}

3 (9^{x}) - 10 (3^{x}) + 3 = 0

3^{2 x + 1} + 3 = 10 (3^{x})

2 e^{12 x} = 17

2^{x} + 2 = 3264

4 - 5^{x} = 0

What is the answer to 4^{-3n-2}*8=16^{3n-2} ?
The answer to 4^{-3n-2}*8=16^{3n-2} is n= 7/18
Solve for n: 4^{-3n-2}*8=16^{3n-2}
The solution is n= 7/18