What is the answer to 2(16^x)-5(4^x)+2=0 ?

The answer to 2(16^x)-5(4^x)+2=0 is x= 1/2 ,x=-1/2

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2(16^x)-5(4^x)+2=0

2 (1 6^{x}) - 5 (4^{x}) + 2 = 0

x = \frac{1}{2}, x = - \frac{1}{2}

Solution steps

2 (1 6^{x}) - 5 (4^{x}) + 2 = 0

Apply exponent rules

2 (4^{x})^{2} - 5 \cdot 4^{x} + 2 = 0

Rewrite the equation with

4^{x} = u

2 (u)^{2} - 5 u + 2 = 0

Solve

2 u^{2} - 5 u + 2 = 0 : u = 2, u = \frac{1}{2}

u = 2, u = \frac{1}{2}

Substitute back

u = 4^{x},

solve for

x

Solve

4^{x} = 2 : x = \frac{1}{2}

Solve

4^{x} = \frac{1}{2} : x = - \frac{1}{2}

x = \frac{1}{2}, x = - \frac{1}{2}

2^{x} + 4^{x} + \frac{1}{4} = 0

100 = 2^{x}

4^{2 x - 3} = 7^{x}

4^{2 x + 3} = 8^{x + 5}

8^{4 n - 2} = 4^{3 n + 3}

What is the answer to 2(16^x)-5(4^x)+2=0 ?
The answer to 2(16^x)-5(4^x)+2=0 is x= 1/2 ,x=-1/2
Solve for x: 2(16^x)-5(4^x)+2=0
The solution is x= 1/2 ,x=-1/2