What is the answer to 6(4^x)-11(2^x)+4=0 ?

The answer to 6(4^x)-11(2^x)+4=0 is x=(ln(4/3))/(ln(2)),x=-1

Solve for x: 6(4^x)-11(2^x)+4=0

The solution is x=(ln(4/3))/(ln(2)),x=-1

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6 (4^{x}) - 11 (2^{x}) + 4 = 0

x = \frac{ln ( \frac{4}{3} )}{ln ( 2 )}, x = - 1

Decimal Notation

x = 0.41503 \dots, x = - 1

Solution steps

6 (4^{x}) - 11 (2^{x}) + 4 = 0

Apply exponent rules

6 (2^{x})^{2} - 11 \cdot 2^{x} + 4 = 0

Rewrite the equation with

2^{x} = u

6 (u)^{2} - 11 u + 4 = 0

Solve

6 u^{2} - 11 u + 4 = 0 : u = \frac{4}{3}, u = \frac{1}{2}

u = \frac{4}{3}, u = \frac{1}{2}

Substitute back

u = 2^{x},

solve for

x

Solve

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

Solve

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

x = \frac{ln ( \frac{4}{3} )}{ln ( 2 )}, x = - 1

6300 = 3130 \cdot 1.0 8^{x}

2^{r} = (\frac{1}{3})^{r - 1}

10 = 2^{\frac{t}{3}}

2 = 1. 2^{x}

5^{5 x + 2} = 15

What is the answer to 6(4^x)-11(2^x)+4=0 ?
The answer to 6(4^x)-11(2^x)+4=0 is x=(ln(4/3))/(ln(2)),x=-1
Solve for x: 6(4^x)-11(2^x)+4=0
The solution is x=(ln(4/3))/(ln(2)),x=-1