What is the answer to 5^{x^2}=25^{x+1} ?

The answer to 5^{x^2}=25^{x+1} is x=1+sqrt(3),x=1-sqrt(3)

Solve for x: 5^{x^2}=25^{x+1}

The solution is x=1+sqrt(3),x=1-sqrt(3)

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

x = 1 + 3, x = 1 - 3

Decimal Notation

x = 2.73205 \dots, x = - 0.73205 \dots

Solution steps

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

Apply exponent rules

x^{2} = 2 (x + 1)

Solve

x^{2} = 2 (x + 1) : x = 1 + 3, x = 1 - 3

x = 1 + 3, x = 1 - 3

5^{2 x} - 5^{x + 1} + 4 = 0

3^{x^{2}} \cdot 3^{5 x} = 729

2 7^{\frac{2}{5}} = 3^{x}

4^{x^{3}} = 2^{54}

3^{x + 1} + 4 = 8

What is the answer to 5^{x^2}=25^{x+1} ?
The answer to 5^{x^2}=25^{x+1} is x=1+sqrt(3),x=1-sqrt(3)
Solve for x: 5^{x^2}=25^{x+1}
The solution is x=1+sqrt(3),x=1-sqrt(3)