What is the answer to 4^x-2^x=6 ?

The answer to 4^x-2^x=6 is x=(ln(3))/(ln(2))

Solve for x: 4^x-2^x=6

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

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4^{x} - 2^{x} = 6

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

Decimal Notation

x = 1.58496 \dots

Solution steps

4^{x} - 2^{x} = 6

Apply exponent rules

(2^{x})^{2} - 2^{x} = 6

Rewrite the equation with

2^{x} = u

(u)^{2} - u = 6

Solve

u^{2} - u = 6 : u = 3, u = - 2

u = 3, u = - 2

Substitute back

u = 2^{x},

solve for

x

Solve

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

Solve

2^{x} = - 2 :

No Solution for

x \in R

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

x, y = 4^{x} y

x, e^{x} = 2^{y}

23 = 520 (0.5)^{\frac{x}{7}}

9^{3 x - 4} = \frac{1}{8 1 ^{2 x - 5}}

3^{x^{2}} = 7