What is the answer to 4^{2x}-68*4^x+256=0 ?

The answer to 4^{2x}-68*4^x+256=0 is x=3,x=1

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4^{2x}-68*4^x+256=0

4^{2 x} - 68 \cdot 4^{x} + 256 = 0

x = 3, x = 1

Solution steps

4^{2 x} - 68 \cdot 4^{x} + 256 = 0

Apply exponent rules

(4^{x})^{2} - 68 \cdot 4^{x} + 256 = 0

Rewrite the equation with

4^{x} = u

(u)^{2} - 68 u + 256 = 0

Solve

u^{2} - 68 u + 256 = 0 : u = 64, u = 4

u = 64, u = 4

Substitute back

u = 4^{x},

solve for

x

Solve

4^{x} = 64 : x = 3

Solve

4^{x} = 4 : x = 1

x = 3, x = 1

x, 4^{3 x} = 4^{x - 1}

3 = 5^{x}

x, 2^{x + 3^{y}} = 11

4^{x} = 256 - 24 (2^{x})

What is the answer to 4^{2x}-68*4^x+256=0 ?
The answer to 4^{2x}-68*4^x+256=0 is x=3,x=1
Solve for x: 4^{2x}-68*4^x+256=0
The solution is x=3,x=1