solve logarithmic equation without numerical methods Is there algebraic method to solve following equation for x: ax+b ln x+c=0 with a,b,c constants without using numerical methods and ln means natural logarithm.

Demarion Ortega

Demarion Ortega

Answered question

2022-11-15

solve logarithmic equation without numerical methods
Is there algebraic method to solve following equation for x:
a x + b ln x + c = 0
with a , b , c constants without using numerical methods and ln means natural logarithm.

Answer & Explanation

iletsa2ym

iletsa2ym

Beginner2022-11-16Added 22 answers

a x + b ln ( x ) + c = 0 a x + b ln ( a b x ) + c b ln ( a b ) = 0 a b x + ln ( a b x ) + c b ln ( a b ) = 0 ( a b ) x e ( a b ) x = ( a b ) e c b
The Lambert-W function is the inverse of x e x .
( a b ) x = W ( ( a b ) e c b )

x = ( b a ) W ( ( a b ) e c b )

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