What is the answer to 5^x+5^{x+3}=A*5^x ?

The answer to 5^x+5^{x+3}=A*5^x is No Solution for x\in\mathbb{R}

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5^x+5^{x+3}=A*5^x

5^{x} + 5^{x + 3} = A \cdot 5^{x}

No Solution for x \in R

Solution steps

5^{x} + 5^{x + 3} = A \cdot 5^{x}

Subtract

A 5^{x}

from both sides

5^{x} + 5^{x + 3} - A \cdot 5^{x} = A \cdot 5^{x} - A \cdot 5^{x}

Simplify

5^{x} + 5^{x + 3} - A \cdot 5^{x} = 0

Factor

5^{x} + 5^{x + 3} - A \cdot 5^{x} : 5^{x} (- A + 126)

5^{x} (- A + 126) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

5^{x} = 0

Solve

5^{x} = 0 :

No Solution for

x \in R

No Solution for x \in R

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

3^{x} \cdot 3^{2 x - 3} = 3^{5}

3^{x} = 1000

3^{4 x} = 81

e^{x^{2} + 2 x} = 2

What is the answer to 5^x+5^{x+3}=A*5^x ?
The answer to 5^x+5^{x+3}=A*5^x is No Solution for x\in\mathbb{R}