What is the answer to (5^{x^2+1})/(25^{x+2)}=3125 ?

The answer to (5^{x^2+1})/(25^{x+2)}=3125 is x=4,x=-2

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(5^{x^2+1})/(25^{x+2)}=3125

\frac{5 ^{x^{2} + 1}}{2 5 ^{x + 2}} = 3125

x = 4, x = - 2

Solution steps

\frac{5 ^{x^{2} + 1}}{2 5 ^{x + 2}} = 3125

Apply exponent rules

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

Solve

x^{2} + 1 + 2 (- x - 2) = 5 : x = 4, x = - 2

x = 4, x = - 2

Verify Solutions:

x = 4

True

, x = - 2

True

The solutions are

x = 4, x = - 2

e^{x^{2}} = 4

- x e^{x} = 0

4 \cdot 1 0^{2 x} = 9

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

9^{x} = \frac{1}{243}

What is the answer to (5^{x^2+1})/(25^{x+2)}=3125 ?
The answer to (5^{x^2+1})/(25^{x+2)}=3125 is x=4,x=-2
Solve for x: (5^{x^2+1})/(25^{x+2)}=3125
The solution is x=4,x=-2