What is the answer to 5^{3x^2}= 1/(25^{5x+2)} ?

The answer to 5^{3x^2}= 1/(25^{5x+2)} is x=(-5+sqrt(13))/3 ,x=-(5+sqrt(13))/3

Solve for x: 5^{3x^2}= 1/(25^{5x+2)}

The solution is x=(-5+sqrt(13))/3 ,x=-(5+sqrt(13))/3

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5^{3 x^{2}} = \frac{1}{2 5 ^{5 x + 2}}

x = \frac{- 5 + 13}{3}, x = - \frac{5 + 13}{3}

Decimal Notation

x = - 0.46481 \dots, x = - 2.86851 \dots

Solution steps

5^{3 x^{2}} = \frac{1}{2 5 ^{5 x + 2}}

Apply exponent rules

3 x^{2} = 2 (- 5 x - 2)

Solve

3 x^{2} = 2 (- 5 x - 2) : x = \frac{- 5 + 13}{3}, x = - \frac{5 + 13}{3}

x = \frac{- 5 + 13}{3}, x = - \frac{5 + 13}{3}

Verify Solutions:

x = \frac{- 5 + 13}{3}

True

, x = - \frac{5 + 13}{3}

True

The solutions are

x = \frac{- 5 + 13}{3}, x = - \frac{5 + 13}{3}

4^{x} - 12 \cdot 2^{x} + 32 = 0

2^{3 x + 1} = 32

e^{x} = 0.5

2^{2 x - 1} = 3^{x + 2}

x, f = (\frac{1}{2})^{x}

What is the answer to 5^{3x^2}= 1/(25^{5x+2)} ?
The answer to 5^{3x^2}= 1/(25^{5x+2)} is x=(-5+sqrt(13))/3 ,x=-(5+sqrt(13))/3
Solve for x: 5^{3x^2}= 1/(25^{5x+2)}
The solution is x=(-5+sqrt(13))/3 ,x=-(5+sqrt(13))/3