What is the answer to 5^x+25^x+125^x=-5 ?

The answer to 5^x+25^x+125^x=-5 is No Solution for x\in\mathbb{R}

Solve for x: 5^x+25^x+125^x=-5

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

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5^{x} + 2 5^{x} + 12 5^{x} = - 5

No Solution for x \in R

Solution steps

5^{x} + 2 5^{x} + 12 5^{x} = - 5

Divide both sides by

5^{x}

\frac{5 ^{x}}{5 ^{x}} + \frac{2 5 ^{x}}{5 ^{x}} + \frac{12 5 ^{x}}{5 ^{x}} = \frac{- 5}{5 ^{x}}

Simplify

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

Apply exponent rules

1 + 5^{x} + (5^{x})^{2} = - (5^{x})^{- 1} \cdot 5^{1}

Rewrite the equation with

5^{x} = u

1 + u + (u)^{2} = - (u)^{- 1} \cdot 5^{1}

Solve

1 + u + u^{2} = - u^{- 1} \cdot 5^{1} : u \approx - 1.88123 \dots

u \approx - 1.88123 \dots

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = - 1.88123 \dots :

No Solution for

x \in R

No Solution for x \in R

y, x = \frac{e ^{y} - e ^{- y}}{2}

5^{x (x - 1)} = 1

e^{3 - 5 x} = 16

y, x = 2^{y}

5^{x + 1} + 5^{x} + 5^{x - 1} = \frac{31}{5}

What is the answer to 5^x+25^x+125^x=-5 ?
The answer to 5^x+25^x+125^x=-5 is No Solution for x\in\mathbb{R}
Solve for x: 5^x+25^x+125^x=-5
The solution is No Solution for x\in\mathbb{R}