What is the answer to 2^{x+2}+2^{x-1}=6^{x-1} ?

The answer to 2^{x+2}+2^{x-1}=6^{x-1} is x=3

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2^{x+2}+2^{x-1}=6^{x-1}

2^{x + 2} + 2^{x - 1} = 6^{x - 1}

x = 3

Solution steps

2^{x + 2} + 2^{x - 1} = 6^{x - 1}

Simplify

2^{x + 2} + 2^{x - 1} : 9 \cdot 2^{x - 1}

9 \cdot 2^{x - 1} = 6^{x - 1}

Apply exponent rules

ln (9) + (x - 1) ln (2) = (x - 1) ln (6)

Solve

ln (9) + (x - 1) ln (2) = (x - 1) ln (6) : x = 3

x = 3

288 \cdot 2^{\frac{x}{4}} = 96

2^{2 x - 3} = 5^{x - 2}

1 0^{- x} = 169

- e^{x} x - 6 e^{x} = 0

3^{x + 1} = 4^{x}

What is the answer to 2^{x+2}+2^{x-1}=6^{x-1} ?
The answer to 2^{x+2}+2^{x-1}=6^{x-1} is x=3
Solve for x: 2^{x+2}+2^{x-1}=6^{x-1}
The solution is x=3