What is the answer to 4^{2x}-65*4^x+64=0 ?

The answer to 4^{2x}-65*4^x+64=0 is x=3,x=0

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4^{2x}-65*4^x+64=0

4^{2 x} - 65 \cdot 4^{x} + 64 = 0

x = 3, x = 0

Solution steps

4^{2 x} - 65 \cdot 4^{x} + 64 = 0

Apply exponent rules

(4^{x})^{2} - 65 \cdot 4^{x} + 64 = 0

Rewrite the equation with

4^{x} = u

(u)^{2} - 65 u + 64 = 0

Solve

u^{2} - 65 u + 64 = 0 : u = 64, u = 1

u = 64, u = 1

Substitute back

u = 4^{x},

solve for

x

Solve

4^{x} = 64 : x = 3

Solve

4^{x} = 1 : x = 0

x = 3, x = 0

e^{4 x} = 4 e^{x}

4^{4 x} = 1 6^{\frac{3}{2} x + 9}

4^{x + 1} + 4^{x - 1} = 34

2. 5^{x} + 4 = 1254

2^{x} - 2 \cdot 4^{x} = 0

What is the answer to 4^{2x}-65*4^x+64=0 ?
The answer to 4^{2x}-65*4^x+64=0 is x=3,x=0
Solve for x: 4^{2x}-65*4^x+64=0
The solution is x=3,x=0