Question Number 14853 by tawa tawa last updated on 04/Jun/17

Solve for x 3^(2x) = 18x

Answered by mrW1 last updated on 04/Jun/17

e^(2xln 3) =18x 18xe^(−2xln 3) =1 (−2xln 3)e^((−2xln 3)) =−((ln 3)/9) ⇒−2xln 3=W(−((ln 3)/9)) ⇒x=−((W(−((ln 3)/9)))/(2ln 3))≈−((W(−0.122068))/(2.197225)) = { ((−((−3.295837)/(2.197225))=1.5)),((−((−0.140479)/(2.197225))=0.063935)) :}

Commented byadelson last updated on 05/Jun/17

what′s W ?

Commented bytawa tawa last updated on 05/Jun/17

God bless you sir.

Commented bymrW1 last updated on 05/Jun/17

W stands for Lambert W−function which is the inverse function of f(x)=xe^x

Commented bytawa tawa last updated on 05/Jun/17

Have been wondering, please sir explain further.

Commented bymrW1 last updated on 05/Jun/17

I don′t know what I can tell more. One should know that for real values W(x) function is defined for x≥−(1/e) and for −(1/e)<x<0 there are two values for W(x).

Commented bytawa tawa last updated on 05/Jun/17

Alright sir. God bless you

Commented bytawa tawa last updated on 05/Jun/17

What i mean is that how do you get − 3.295837

Commented bymrW1 last updated on 06/Jun/17

if you can not find a W−function calculator which gives 2 values for x<0, you can also calculate by youself, for example using geogebra. you find just the zero points from function f(x)=xe^x +((ln 3)/9)

Commented bymrW1 last updated on 06/Jun/17

Commented bytawa tawa last updated on 06/Jun/17

God bless you sir.