What is the answer to 8^{2x}-10(8^x)+16=0 ?

The answer to 8^{2x}-10(8^x)+16=0 is x=1,x= 1/3

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8^{2x}-10(8^x)+16=0

8^{2 x} - 10 (8^{x}) + 16 = 0

x = 1, x = \frac{1}{3}

Solution steps

8^{2 x} - 10 (8^{x}) + 16 = 0

Apply exponent rules

(8^{x})^{2} - 10 \cdot 8^{x} + 16 = 0

Rewrite the equation with

8^{x} = u

(u)^{2} - 10 u + 16 = 0

Solve

u^{2} - 10 u + 16 = 0 : u = 8, u = 2

u = 8, u = 2

Substitute back

u = 8^{x},

solve for

x

Solve

8^{x} = 8 : x = 1

Solve

8^{x} = 2 : x = \frac{1}{3}

x = 1, x = \frac{1}{3}

1 6^{x} = \frac{1}{8}

2^{x} \cdot 3^{x} = 216

e^{7 x} = 7 e^{x}

e^{2 x} + e^{x} = 6

e^{x + 2} = (e^{x - 1})^{2}

What is the answer to 8^{2x}-10(8^x)+16=0 ?
The answer to 8^{2x}-10(8^x)+16=0 is x=1,x= 1/3
Solve for x: 8^{2x}-10(8^x)+16=0
The solution is x=1,x= 1/3