What is the answer to 5^{x+1}+5^x+5^{x-2}-151=0 ?

The answer to 5^{x+1}+5^x+5^{x-2}-151=0 is x=2

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5^{x+1}+5^x+5^{x-2}-151=0

5^{x + 1} + 5^{x} + 5^{x - 2} - 151 = 0

x = 2

Solution steps

5^{x + 1} + 5^{x} + 5^{x - 2} - 151 = 0

Factor

5^{x + 1} + 5^{x} + 5^{x - 2} - 151 : 151 (5^{x - 2} - 1)

151 (5^{x - 2} - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

5^{x - 2} - 1 = 0

Solve

5^{x - 2} - 1 = 0 : x = 2

x = 2

2^{2 x} - 2^{x} - 12 = 0

4 + 3^{5 x} = 8

(\frac{1}{8})^{x + 3} = 1 6^{x - 4}

e^{\frac{2 x}{5}} = 25

e^{2 x} + 3 e^{x} = 18

What is the answer to 5^{x+1}+5^x+5^{x-2}-151=0 ?
The answer to 5^{x+1}+5^x+5^{x-2}-151=0 is x=2
Solve for x: 5^{x+1}+5^x+5^{x-2}-151=0
The solution is x=2