What is the answer to (1/12)^{x-2}=2^{4*x}*3^{2*x} ?

The answer to (1/12)^{x-2}=2^{4*x}*3^{2*x} is x= 2/3

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(1/12)^{x-2}=2^{4x}3^{2*x}

(\frac{1}{12})^{x - 2} = 2^{4 \cdot x} \cdot 3^{2 \cdot x}

x = \frac{2}{3}

Decimal Notation

x = 0.66666 \dots

Solution steps

(\frac{1}{12})^{x - 2} = 2^{4 x} \cdot 3^{2 x}

Apply exponent rules

(x - 2) ln (\frac{1}{12}) = (4 x + lo g_{2} (3) \cdot 2 x) ln (2)

Solve

(x - 2) ln (\frac{1}{12}) = (4 x + lo g_{2} (3) \cdot 2 x) ln (2) : x = \frac{2}{3}

x = \frac{2}{3}

2 \cdot 3^{x + 1} + 3^{x + 3} = 33

x, 2^{x + 1} - 1 = 7^{y}

2^{4 x + 3} = 8^{x - 5}

5^{2 x + 1} = 3^{4 x - 1}

2 e^{0.5} x = e^{x}

What is the answer to (1/12)^{x-2}=2^{4*x}*3^{2*x} ?
The answer to (1/12)^{x-2}=2^{4*x}*3^{2*x} is x= 2/3
Solve for x: (1/12)^{x-2}=2^{4*x}*3^{2*x}
The solution is x= 2/3