What is the answer to 16^x-4^{x+1}+3=0 ?

The answer to 16^x-4^{x+1}+3=0 is x=(ln(3))/(2ln(2)),x=0

Solve for x: 16^x-4^{x+1}+3=0

The solution is x=(ln(3))/(2ln(2)),x=0

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1 6^{x} - 4^{x + 1} + 3 = 0

x = \frac{ln ( 3 )}{2 ln ( 2 )}, x = 0

Decimal Notation

x = 0.79248 \dots, x = 0

Solution steps

1 6^{x} - 4^{x + 1} + 3 = 0

Apply exponent rules

(4^{x})^{2} - 4^{x} \cdot 4^{1} + 3 = 0

Rewrite the equation with

4^{x} = u

(u)^{2} - u \cdot 4^{1} + 3 = 0

Solve

u^{2} - u \cdot 4^{1} + 3 = 0 : u = 3, u = 1

u = 3, u = 1

Substitute back

u = 4^{x},

solve for

x

Solve

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

Solve

4^{x} = 1 : x = 0

x = \frac{ln ( 3 )}{2 ln ( 2 )}, x = 0

625 = 5^{6 - 2 x}

2400 = 7500 (10)^{- x}

e^{6 a + 5} = 11

4^{4 x - 5} = 16

45 = 21 + 1079 \cdot e^{x \cdot 20}

What is the answer to 16^x-4^{x+1}+3=0 ?
The answer to 16^x-4^{x+1}+3=0 is x=(ln(3))/(2ln(2)),x=0
Solve for x: 16^x-4^{x+1}+3=0
The solution is x=(ln(3))/(2ln(2)),x=0