What is the answer to 27^{2x}=9^{x-3} ?

The answer to 27^{2x}=9^{x-3} is x=-3/2

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27^{2x}=9^{x-3}

2 7^{2 x} = 9^{x - 3}

x = - \frac{3}{2}

Decimal Notation

x = - 1.5

Solution steps

2 7^{2 x} = 9^{x - 3}

Apply exponent rules

6 x = 2 (x - 3)

Solve

6 x = 2 (x - 3) : x = - \frac{3}{2}

x = - \frac{3}{2}

e^{x} - 5 e^{- x} + 4 e^{- 3 x} = 0

e^{x} = x

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

8^{x + 1} + 8^{1 - x} = 20

e^{3 x + 1} = 10