What is the answer to 3^x-3^{x-1}-7*3^{x-3}=33 ?

The answer to 3^x-3^{x-1}-7*3^{x-3}=33 is x=4

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3^x-3^{x-1}-7*3^{x-3}=33

3^{x} - 3^{x - 1} - 7 \cdot 3^{x - 3} = 33

x = 4

Solution steps

3^{x} - 3^{x - 1} - 7 \cdot 3^{x - 3} = 33

Factor

3^{x} - 3^{x - 1} - 7 \cdot 3^{x - 3} : 11 \cdot 3^{x - 3}

11 \cdot 3^{x - 3} = 33

Divide both sides by

11

3^{x - 3} = 3

Apply exponent rules

x - 3 = 1

Solve

x - 3 = 1 : x = 4

x = 4

x, z = e^{x y}

2^{x - 1} - 2^{x + 3} + 2^{x} = - \frac{13}{8}

3^{x} = 3 \frac{1}{4}

3 e^{- x} x^{2} - e^{- x} x^{3} = 0

8^{x + 3} = \frac{1}{16}

What is the answer to 3^x-3^{x-1}-7*3^{x-3}=33 ?
The answer to 3^x-3^{x-1}-7*3^{x-3}=33 is x=4
Solve for x: 3^x-3^{x-1}-7*3^{x-3}=33
The solution is x=4