What is the answer to 4^x-20*2^x+64=0 ?

The answer to 4^x-20*2^x+64=0 is x=4,x=2

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4^x-20*2^x+64=0

4^{x} - 20 \cdot 2^{x} + 64 = 0

x = 4, x = 2

Solution steps

4^{x} - 20 \cdot 2^{x} + 64 = 0

Apply exponent rules

(2^{x})^{2} - 20 \cdot 2^{x} + 64 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} - 20 u + 64 = 0

Solve

u^{2} - 20 u + 64 = 0 : u = 16, u = 4

u = 16, u = 4

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 16 : x = 4

Solve

2^{x} = 4 : x = 2

x = 4, x = 2

7^{x} = e^{x + 6}

7^{x} = e^{x + 4}

e^{2 x} = \frac{1}{e}

e^{3 x} = 6

e^{3 x} = 7

What is the answer to 4^x-20*2^x+64=0 ?
The answer to 4^x-20*2^x+64=0 is x=4,x=2
Solve for x: 4^x-20*2^x+64=0
The solution is x=4,x=2