What is the answer to 4^x+4^{x-1}-4^{x+1}+44=0 ?

The answer to 4^x+4^{x-1}-4^{x+1}+44=0 is x=2

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4^x+4^{x-1}-4^{x+1}+44=0

4^{x} + 4^{x - 1} - 4^{x + 1} + 44 = 0

x = 2

Solution steps

4^{x} + 4^{x - 1} - 4^{x + 1} + 44 = 0

Factor

4^{x} + 4^{x - 1} - 4^{x + 1} + 44 : 11 (- 4^{x - 1} + 4)

11 (- 4^{x - 1} + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

- 4^{x - 1} + 4 = 0

Solve

- 4^{x - 1} + 4 = 0 : x = 2

x = 2

4^{5 x - 13} = \frac{1}{8 ^{x}}

2 e^{2 x} + 9 e^{x} = 5

5^{x - 9} = 0.2

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

4^{x + 1} = 256

What is the answer to 4^x+4^{x-1}-4^{x+1}+44=0 ?
The answer to 4^x+4^{x-1}-4^{x+1}+44=0 is x=2
Solve for x: 4^x+4^{x-1}-4^{x+1}+44=0
The solution is x=2