What is the answer to 2(2^2)^x-10(2^x)+12=0 ?

The answer to 2(2^2)^x-10(2^x)+12=0 is x=(ln(3))/(ln(2)),x=1

Solve for x: 2(2^2)^x-10(2^x)+12=0

The solution is x=(ln(3))/(ln(2)),x=1

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2 (2^{2})^{x} - 10 (2^{x}) + 12 = 0

x = \frac{ln ( 3 )}{ln ( 2 )}, x = 1

Decimal Notation

x = 1.58496 \dots, x = 1

Solution steps

2 (2^{2})^{x} - 10 (2^{x}) + 12 = 0

Apply exponent rules

(2^{x})^{2} \cdot 2^{1} - 10 \cdot 2^{x} + 12 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} \cdot 2^{1} - 10 u + 12 = 0

Solve

u^{2} \cdot 2^{1} - 10 u + 12 = 0 : u = 3, u = 2

u = 3, u = 2

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 3 : x = \frac{ln ( 3 )}{ln ( 2 )}

Solve

2^{x} = 2 : x = 1

x = \frac{ln ( 3 )}{ln ( 2 )}, x = 1

5^{x - 2} = 3^{3 x + 2}

3^{2 x} = 9

2^{5 x} = 3^{2 x + 1}

2^{x - 1} = 1

81 = 3^{x}

What is the answer to 2(2^2)^x-10(2^x)+12=0 ?
The answer to 2(2^2)^x-10(2^x)+12=0 is x=(ln(3))/(ln(2)),x=1
Solve for x: 2(2^2)^x-10(2^x)+12=0
The solution is x=(ln(3))/(ln(2)),x=1