What is the answer to 4^x-2^{x+1}=3 ?

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

Solve for x: 4^x-2^{x+1}=3

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

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4^{x} - 2^{x + 1} = 3

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

Decimal Notation

x = 1.58496 \dots

Solution steps

4^{x} - 2^{x + 1} = 3

Apply exponent rules

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

Rewrite the equation with

2^{x} = u

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

Solve

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

u = 3, u = - 1

Substitute back

u = 2^{x},

solve for

x

Solve

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

Solve

2^{x} = - 1 :

No Solution for

x \in R

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

9^{x} = - 3

62 \cdot 2^{5 x} = 27

3^{x} = 6561

8^{x} = 12143

2^{x - 1} = 2^{x} - 8

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