What is the answer to 4^{2x}-5*4^{x+2}+1021=0 ?

The answer to 4^{2x}-5*4^{x+2}+1021=0 is x=(ln(40+sqrt(579)))/(2ln(2)),x=(ln(40-sqrt(579)))/(2ln(2))

Solve for x: 4^{2x}-5*4^{x+2}+1021=0

The solution is x=(ln(40+sqrt(579)))/(2ln(2)),x=(ln(40-sqrt(579)))/(2ln(2))

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4^{2 x} - 5 \cdot 4^{x + 2} + 1021 = 0

x = \frac{ln ( 40 + 579 )}{2 ln ( 2 )}, x = \frac{ln ( 40 - 579 )}{2 ln ( 2 )}

Decimal Notation

x = 3.00070 \dots, x = 1.99718 \dots

Solution steps

4^{2 x} - 5 \cdot 4^{x + 2} + 1021 = 0

Apply exponent rules

(4^{x})^{2} - 5 \cdot 4^{x} \cdot 4^{2} + 1021 = 0

Rewrite the equation with

4^{x} = u

(u)^{2} - 5 u \cdot 4^{2} + 1021 = 0

Solve

u^{2} - 5 u \cdot 4^{2} + 1021 = 0 : u = 40 + 579, u = 40 - 579

u = 40 + 579, u = 40 - 579

Substitute back

u = 4^{x},

solve for

x

Solve

4^{x} = 40 + 579 : x = \frac{ln ( 40 + 579 )}{2 ln ( 2 )}

Solve

4^{x} = 40 - 579 : x = \frac{ln ( 40 - 579 )}{2 ln ( 2 )}

x = \frac{ln ( 40 + 579 )}{2 ln ( 2 )}, x = \frac{ln ( 40 - 579 )}{2 ln ( 2 )}

5^{3 x + 2} - 3 \cdot 5^{6 x + 2} - 100 = 0

3 \cdot 6^{x} = 4.5 (e^{2})^{x}

x, 3^{x} = 27

x, 3^{x} = 81

3^{x} = 7^{1 - x}

What is the answer to 4^{2x}-5*4^{x+2}+1021=0 ?
The answer to 4^{2x}-5*4^{x+2}+1021=0 is x=(ln(40+sqrt(579)))/(2ln(2)),x=(ln(40-sqrt(579)))/(2ln(2))
Solve for x: 4^{2x}-5*4^{x+2}+1021=0
The solution is x=(ln(40+sqrt(579)))/(2ln(2)),x=(ln(40-sqrt(579)))/(2ln(2))