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

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

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5^x+5^{2x-2}-25^{x-1}=5^{2x-3}

5^{x} + 5^{2 x - 2} - 2 5^{x - 1} = 5^{2 x - 3}

x = 3

Solution steps

5^{x} + 5^{2 x - 2} - 2 5^{x - 1} = 5^{2 x - 3}

Move

5^{2 x - 3}

to the left side

5^{x} + 4 \cdot 5^{2 x - 3} - 2 5^{x - 1} = 0

Move

2 5^{x - 1}

to the right side

5^{x} + 4 \cdot 5^{2 x - 3} = 2 5^{x - 1}

Apply exponent rules

5^{x} + 4 (5^{x})^{2} \cdot 5^{- 3} = (5^{x})^{2} \cdot 5^{- 2}

Rewrite the equation with

5^{x} = u

u + 4 (u)^{2} \cdot 5^{- 3} = (u)^{2} \cdot 5^{- 2}

Solve

u + 4 u^{2} \cdot 5^{- 3} = u^{2} \cdot 5^{- 2} : u = 0, u = 125

u = 0, u = 125

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 0 :

No Solution for

x \in R

Solve

5^{x} = 125 : x = 3

x = 3

x, z^{2} = 3^{10} + 3^{x}

3 (1 2^{- 11 - x}) + 8 = 2501

e^{x} - e^{- x} - 6 = - 10

3^{x} + 20 = 28

y, e^{x + 2 y} = 0

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