What is the answer to 2x-1sqrt(3^{x-3)}=sqrt(27) ?

The answer to 2x-1sqrt(3^{x-3)}=sqrt(27) is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2x-1sqrt(3^{x-3)}=sqrt(27)

2 x - 1 3^{x - 3} = 27

x = \frac{2 ln - \frac{4 W _{- 1} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3, x = \frac{2 ln - \frac{4 W _{0} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3

Decimal Notation

x = 6.93121 \dots, x = 3.13722 \dots

Solution steps

2 x - 1 \cdot 3^{x - 3} = 27

Rewrite the equation with

3^{x - 3} = u

and

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

2 (\frac{2 ln ( u )}{ln ( 3 )} + 3) - 1 \cdot u = 27

Solve

2 (\frac{2 ln ( u )}{ln ( 3 )} + 3) - 1 \cdot u = 27 : u = - \frac{4 W _{- 1} ( - \frac{l n ( 3 )}{4 e ^{\frac{6 l n ( 3 ) - 3 3 l n ( 3 )}{4}}} )}{ln ( 3 )}, u = - \frac{4 W _{0} ( - \frac{l n ( 3 )}{4 e ^{\frac{6 l n ( 3 ) - 3 3 l n ( 3 )}{4}}} )}{ln ( 3 )}

u = - \frac{4 W _{- 1} ( - \frac{l n ( 3 )}{4 e ^{\frac{6 l n ( 3 ) - 3 3 l n ( 3 )}{4}}} )}{ln ( 3 )}, u = - \frac{4 W _{0} ( - \frac{l n ( 3 )}{4 e ^{\frac{6 l n ( 3 ) - 3 3 l n ( 3 )}{4}}} )}{ln ( 3 )}

Substitute back

u = 3^{x - 3},

solve for

x

Solve

3^{x - 3} = - \frac{4 W _{- 1} ( - \frac{l n ( 3 )}{4 e ^{\frac{6 l n ( 3 ) - 3 3 l n ( 3 )}{4}}} )}{ln ( 3 )} : x = \frac{2 ln - \frac{4 W _{- 1} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3

Solve

3^{x - 3} = - \frac{4 W _{0} ( - \frac{l n ( 3 )}{4 e ^{\frac{6 l n ( 3 ) - 3 3 l n ( 3 )}{4}}} )}{ln ( 3 )} : x = \frac{2 ln - \frac{4 W _{0} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3

x = \frac{2 ln - \frac{4 W _{- 1} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3, x = \frac{2 ln - \frac{4 W _{0} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3

Verify Solutions:

x = \frac{2 ln - \frac{4 W _{- 1} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3

True

, x = \frac{2 ln - \frac{4 W _{0} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3

True

The solutions are

x = \frac{2 ln - \frac{4 W _{- 1} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3, x = \frac{2 ln - \frac{4 W _{0} ( - \frac{l n ( 3 ) e ^{- \frac{6 l n ( 3 ) - 3 l n ( 3 )}{4}}}{4} )}{l n ( 3 )}}{ln ( 3 )} + 3

x = 3 + 23 - x

x, z = 4 - x^{2} - y^{2}

p - 10 = 50 - 5 p

y, x + y = 5

y, x + y = 6

What is the answer to 2x-1sqrt(3^{x-3)}=sqrt(27) ?
The answer to 2x-1sqrt(3^{x-3)}=sqrt(27) is
Solve for x: 2x-1sqrt(3^{x-3)}=sqrt(27)
The solution is