What is the answer to (2^x)/(512)=(2^x)^4 ?

The answer to (2^x)/(512)=(2^x)^4 is x=-3

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(2^x)/(512)=(2^x)^4

\frac{2 ^{x}}{512} = (2^{x})^{4}

x = - 3

Solution steps

\frac{2 ^{x}}{512} = (2^{x})^{4}

Multiply both sides by

512

\frac{2 ^{x}}{512} \cdot 512 = (2^{x})^{4} \cdot 512

Simplify

2^{x} = 512 (2^{x})^{4}

Apply exponent rules

x = x \cdot 4 + 9

Solve

x = x \cdot 4 + 9 : x = - 3

x = - 3

7^{1 - x} = 3^{2 x + 1}

(2)^{x + 2} = (0.5)^{2 x - 4}

100 = e^{- 9 t + 3 l n (2)}

5^{x} = e^{x - 1}

x^{l o g_{5} (x) - 2} = 125

What is the answer to (2^x)/(512)=(2^x)^4 ?
The answer to (2^x)/(512)=(2^x)^4 is x=-3
Solve for x: (2^x)/(512)=(2^x)^4
The solution is x=-3