What is the answer to 2^x+4^x+1/4 =0 ?

The answer to 2^x+4^x+1/4 =0 is No Solution for x\in\mathbb{R}

Solve for x: 2^x+4^x+1/4 =0

The solution is No Solution for x\in\mathbb{R}

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2^{x} + 4^{x} + \frac{1}{4} = 0

No Solution for x \in R

Solution steps

2^{x} + 4^{x} + \frac{1}{4} = 0

Apply exponent rules

2^{x} + (2^{x})^{2} + \frac{1}{4} = 0

Rewrite the equation with

2^{x} = u

u + (u)^{2} + \frac{1}{4} = 0

Solve

u + u^{2} + \frac{1}{4} = 0 : u = - \frac{1}{2}

u = - \frac{1}{2}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = - \frac{1}{2} :

No Solution for

x \in R

No Solution for x \in R

100 = 2^{x}

4^{2 x - 3} = 7^{x}

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

8^{4 n - 2} = 4^{3 n + 3}

(x^{2} - 5) (e^{x} - 5) = 0

What is the answer to 2^x+4^x+1/4 =0 ?
The answer to 2^x+4^x+1/4 =0 is No Solution for x\in\mathbb{R}
Solve for x: 2^x+4^x+1/4 =0
The solution is No Solution for x\in\mathbb{R}