solve for k: (1/3)(e^3/2x) +(4/9k)(e^3/2k)=0

Question

1/3e

e=2.718281828

 

Answer 1

I will assume that by (1/3)(e^3/2x) +(4/9k)(e^3/2k)=0  you meant:

 

(1/3)e^(3k/2) + (4k/9)e^(3k/2) = 0       (I assumed that x was a typo- that it was meant to be k)

 

The first thing to do is to factor e^(3k/2) out of the left hand side.

So you have:   ( 1/3 + 4k/9 )(e^3k/2) = 0

This implies that either 1/3 + 4k/9  equals zero or that e^(3k/2) equals zero.

Exponential functions will never equal zero, so we may disregard the e^(3k/2) while solving this equation.

 

1/3 + 4k/9 = 0 

 

3+ 4k = 0

 

k= -3/4