Understanding Ln Graph: Form & Deduction of P and L in V = Pe-LQ

[georgiemuc]

If V = Pe^-LQ
Where P and L are constants,

Describe the form that a graph of lnV against Q should take and explain how P and L can be deduced?

Very very stuck, please help!

 

[MalachiK]

If you take logs of both sides

Ln(V) = Ln(Pe^-LQ)

you should then be able to apply the rules for dealing with logs to the equation and go from there.

 

[georgiemuc]

If you take logs of both sides

Ln(V) = Ln(Pe^-LQ)

you should then be able to apply the rules for dealing with logs to the equation and go from there.

I have tried this and just got myself in a massive mess haha, any help?

 

[MalachiK]

You should post what you have done so that we can see where the problem is. the left hand side is just Ln(V), nothing has to happen to that. On the right you have two terms multiplied by each other.

You know that in general ln(AB) = ln(A) + ln(B), apply this and you should get something that looks like the equation of a straight line... remember y = mx + c?

 

[rwisz]

I am happy to assist you in understanding the form and deduction of P and L in the equation V = Pe-LQ. First, it is important to understand that lnV represents the natural logarithm of V, which is a mathematical function used to describe the relationship between two variables. In this case, V is dependent on Q, and lnV is plotted against Q on a graph.

The form of the graph of lnV against Q should be a straight line with a negative slope. This is because lnV is inversely proportional to Q, meaning as Q increases, lnV decreases. This relationship is represented by the negative sign in front of L in the equation. The value of P in the equation represents the y-intercept of the graph, which is the value of lnV when Q is equal to zero.

To deduce the values of P and L from the graph, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. In our case, the equation would be lnV = -LQ + P. By comparing this equation to the slope-intercept form, we can see that the slope is -L and the y-intercept is P. Therefore, the values of P and L can be deduced from the slope and y-intercept of the graph of lnV against Q.

In conclusion, the form of the graph of lnV against Q is a straight line with a negative slope, and the values of P and L can be deduced from the slope and y-intercept of the graph. I hope this explanation helps in your understanding of the ln graph and the deduction of P and L in the given equation.