What is the answer to 16^x-5(4^x)+6=0 ?

The answer to 16^x-5(4^x)+6=0 is x=(ln(3))/(2ln(2)),x= 1/2

Solve for x: 16^x-5(4^x)+6=0

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

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1 6^{x} - 5 (4^{x}) + 6 = 0

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

Decimal Notation

x = 0.79248 \dots, x = 0.5

Solution steps

1 6^{x} - 5 (4^{x}) + 6 = 0

Apply exponent rules

(4^{x})^{2} - 5 \cdot 4^{x} + 6 = 0

Rewrite the equation with

4^{x} = u

(u)^{2} - 5 u + 6 = 0

Solve

u^{2} - 5 u + 6 = 0 : u = 3, u = 2

u = 3, u = 2

Substitute back

u = 4^{x},

solve for

x

Solve

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

Solve

4^{x} = 2 : x = \frac{1}{2}

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

e^{x} = 4 x^{2 + 10}

10 = 5 e^{5 x}

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

e^{- 3} e^{2} ln (e^{e}) = e^{x}

5^{x^{2}} = 17

What is the answer to 16^x-5(4^x)+6=0 ?
The answer to 16^x-5(4^x)+6=0 is x=(ln(3))/(2ln(2)),x= 1/2
Solve for x: 16^x-5(4^x)+6=0
The solution is x=(ln(3))/(2ln(2)),x= 1/2