Logarithmic function

[Matthew Ko]

Hi,
I've been struggling with this logarithmic problem. My attempted work is attached along with the problem. Even after I've done my last step, I noticed that I still can't isolate the variable a in order to solve for it. Could someone please help me? Thank you for your time in reading this post.

 

[Deleted member 4993]

Hi,
I've been struggling with this logarithmic problem. My attempted work is attached along with the problem. Even after I've done my last step, I noticed that I still can't isolate the variable a in order to solve for it. Could someone please help me? Thank you for your time in reading this post.

Did your Assignment expect an

EXACT answer or

an approximate answer

 

[HallsofIvy]

Do you know and can you use the "Lambert W function"?

 

[Matthew Ko]

Did your Assignment expect an

EXACT answer or

an approximate answer

Thank you so much for helping me.

An approximate answer would suffice for the moment, sir/madam.

 

[Matthew Ko]

Do you know and can you use the "Lambert W function"?

Thank you so much for helping me.

I searched the function in Google and came to understand why Subhotosh Khan would ask me if I wanted either an exact or approximate answer. For the moment, however (as mentioned), I would like to know how to solve for an approximate answer.

 

[Deleted member 4993]

Thank you so much for helping me.

An approximate answer would suffice for the moment, sir/madam.

What method have you been taught to estimate the roots of a function?

First plot the function for a domain of say -5≤x≤5 and observe the nature of the curve.

 

[HallsofIvy]

Oh, dear! Using "Desmos", https://www.desmos.com/calculator, to graph this function, it appears that the graph never crosses the x-axis so there is NO value of x satisfyig \(\displaystyle 1.5a+ ln\left(\frac{a+ 1.5}{a}\right)+1.125= 0\).

 

[Deleted member 4993]

Hi,
I've been struggling with this logarithmic problem. My attempted work is attached along with the problem. Even after I've done my last step, I noticed that I still can't isolate the variable a in order to solve for it. Could someone please help me? Thank you for your time in reading this post.

If I were the instructor who assigned this problem, I would expect you to first plot:

y = 1.5 * x + ln[(x + 1.5)/x] + 1.125

then decide about path-forward

 

[Deleted member 4993]

That is why I was surprised when you asked about

"Lambert function"!(response #3)​