Solve the equation. $$ 2^{4 x+1}=4 $$ The solution set is $$ \{\square $$. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

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UpStudy AI · Accepted Answer

We start with the equation

$$
2^{4x+1} = 4.
$$

Since $$4$$ can be written as a power of $$2$$ (because $$4 = 2^2$$), we have

$$
2^{4x+1} = 2^2.
$$

Because the bases are the same, the exponents must be equal:

$$
4x + 1 = 2.
$$

Subtracting $$1$$ from both sides gives

$$
4x = 1.
$$

Dividing both sides by $$4$$ yields

$$
x = \frac{1}{4}.
$$

Thus, the solution set is

$$
\left\{ \frac{1}{4} \right\}.
$$
The solution is $$ x = \frac{1}{4} $$.

Solve the equation.

The solution set is .
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

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Solve the equation. The solution set is . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)