What is the answer to 5^{x+2}+3*5^{x+1}-8=0 ?

The answer to 5^{x+2}+3*5^{x+1}-8=0 is x=-1

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5^{x+2}+3*5^{x+1}-8=0

5^{x + 2} + 3 \cdot 5^{x + 1} - 8 = 0

x = - 1

Solution steps

5^{x + 2} + 3 \cdot 5^{x + 1} - 8 = 0

Factor

5^{x + 2} + 3 \cdot 5^{x + 1} - 8 : 8 (5^{1 + x} - 1)

8 (5^{1 + x} - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

5^{1 + x} - 1 = 0

Solve

5^{1 + x} - 1 = 0 : x = - 1

x = - 1

0.6 4^{- 5 x + 1} = 0.51 2^{- 5 x + 4}

16 = 8^{x}

2 x e^{- x} + (- e^{- x}) x^{2} = 0

1 0^{\frac{x}{3}} = 20

3^{x + 1} + 3^{x + 2} + 3^{x + 3} = 351

What is the answer to 5^{x+2}+3*5^{x+1}-8=0 ?
The answer to 5^{x+2}+3*5^{x+1}-8=0 is x=-1
Solve for x: 5^{x+2}+3*5^{x+1}-8=0
The solution is x=-1