What is the answer to 2^{2x}+2x-6=0 ?

The answer to 2^{2x}+2x-6=0 is x=1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2^{2x}+2x-6=0

2^{2 x} + 2 x - 6 = 0

x = 1

Solution steps

2^{2 x} + 2 x - 6 = 0

Prepare

2^{2 x} + 2 x - 6 = 0

for Lambert form:

1 = - e^{- 2 l n (2) x} (2 x - 6)

Rewrite the equation with

2 ln (2) (- x + 3) = u

and

x = - \frac{u - 6 ln ( 2 )}{2 ln ( 2 )}

1 = - e^{- 2 l n (2) (- \frac{u - 6 l n ( 2 )}{2 l n ( 2 )})} (2 (- \frac{u - 6 ln ( 2 )}{2 ln ( 2 )}) - 6)

Simplify

1 = - e^{u - 6 l n (2)} (- \frac{u - 6 ln ( 2 )}{ln ( 2 )} - 6)

Rewrite

1 = - e^{u - 6 l n (2)} (- \frac{u - 6 ln ( 2 )}{ln ( 2 )} - 6)

in Lambert form:

e^{u} u = 64 ln (2)

Solve

e^{u} u = 64 ln (2) : u = 4 ln (2)

u = 4 ln (2)

Substitute back

u = 2 ln (2) (- x + 3),

solve for

x

Solve

2 ln (2) (- x + 3) = 4 ln (2) : x = 1

x = 1

9 (2.3)^{3 x} = 18

3^{x + 2} = 729

118.85 \cdot 1. 2^{x} = 550

2^{e a} = a

100 = 96.87 e^{r}