What is the answer to 2^x-2=-2x+12 ?

The answer to 2^x-2=-2x+12 is x=3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2^x-2=-2x+12

2^{x} - 2 = - 2 x + 12

x = 3

Solution steps

2^{x} - 2 = - 2 x + 12

Prepare

2^{x} - 2 = - 2 x + 12

for Lambert form:

1 = (- 2 x + 14) e^{- l n (2) x}

Rewrite the equation with

(- x + 7) ln (2) = u

and

x = - \frac{u - 7 ln ( 2 )}{ln ( 2 )}

1 = (- 2 (- \frac{u - 7 ln ( 2 )}{ln ( 2 )}) + 14) e^{- l n (2) (- \frac{u - 7 l n ( 2 )}{l n ( 2 )})}

Simplify

1 = e^{u - 7 l n (2)} (\frac{2 ( u - 7 ln ( 2 ) )}{ln ( 2 )} + 14)

Rewrite

1 = e^{u - 7 l n (2)} (\frac{2 ( u - 7 ln ( 2 ) )}{ln ( 2 )} + 14)

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 = (- x + 7) ln (2),

solve for

x

Solve

(- x + 7) ln (2) = 4 ln (2) : x = 3

x = 3

7^{x - 2} = 49

22000 e^{0.05 t} = 11000 e^{0.07 t}

1 6^{x} = 8^{6}

1000000 = 500000 (1.0375)^{x}

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