Formulae with logarithmic terms

[brenfox]

Homework Statement

w = 1/h ln(l/lo-1)
w=-2.6, lo=16 and h =1.5 Find L.

Homework Equations

The Attempt at a Solution

Plug in the values
2.6 = 1/1.5 ln(l/16 - 1)
Make the log term the subject.
ln(L/16 -1) = 1/1.5/-2.6
ln(L/16-1) = 0.666/-0.256
ln(L/16-1) = -0.256

Change the log statement to an index statement

L/16-1 = e^-0.256
Get L on its own
L = e^-0.256x16+1
L = 13.386
Am I on the right track?

 

[BvU]

You can check by filling in the numbers, right?
First stumble is then that L/l₀-1 < 0 and you can't take the ln of a negative number.
Conclusion: you're off the right track. Can you see where this last error popped up ?
Correct it and try again (check by filling in the numbers)

 

[brenfox]

Forgot to plug in my answer! I will have another look at it. Seems like I am way off so will have to do a bit more reading into it. Thanks for the reply.

 

[brenfox]

Yes. Just plugged in my answer and calculator shows error. So L must be bigger than 16.

 

[BvU]

L/16-1 = e^-0.256
Get L on its own
L = e^-0.256x16+1

Do this one step at a time

Then check - and if it still doesn't fit:

2.6 = 1/1.5 ln(l/16 - 1)
Make the log term the subject.
ln(L/16 -1) = 1/1.5/-2.6

Check this step.

 

[brenfox]

L/16 -1 = e^-0.256

L -1 = e^-0.256 x 16

L = 1 e^-0.256 x 16

L = 1 + 0.774 x 16 = 28.3284. This is also wrong when i plug it in.

 

[Maged Saeed]

ln(L/16 -1) = 1/1.5/-2.6

L/16 -1 = e^-0.256

L -1 = e^-0.256 x 16

Is $\frac{L}{16}-1=e^{-0.256}$ EQUIVALENT TO $L - 1=e^{-0.256} \times 16$?

Why didn't you multiply [1] by [16] ??

 

[SammyS]

...

2.6 = 1/1.5 ln(l/16 - 1)
Make the log term the subject.
ln(L/16 -1) = 1/1.5/-2.6
...

To make the log term the subject, why not simply multiply (both sides) by 1.5 ?

 

[brenfox]

I am starting to confuse myself here!

The equation is -2.6 = 1/1.5 ln(L/Lo -1)

multiply both sides by 1.5

-2.6x1.5 = ln(L/16 -1)

-3.9= ln(L/16-1)

L/16-1 e^-39

L/16 -1 = 0.02

L-1 =0.02 x 16

L = 0.02x16 +1
L= 1.32. I know i am going wrong somewhere because my answer does not plug into the original equation?

 

[Maged Saeed]

L/16 -1 = 0.02

L-1 =0.02 x 16

Again ,, Why don't you multiply 1 by 16 ?
You have to multiply 16 By each term in the equation ,, RIGHT ,,!

 

[brenfox]

If L-1 = 0.02 x 16 Then to get L on its own does the -1 turn into 1 on the other side of the equation? I can`t see the wood for the trees on this one.

 

[Maged Saeed]

If L-1 = 0.02 x 16 Then to get L on its own does the -1 turn into 1 on the other side of the equation? I can`t see the wood for the trees on this one.

-2.6x1.5 = ln(L/16 -1)

-3.9= ln(L/16-1)

L/16-1 = e^-3.9

L/16 -1 = 0.02 [Multiply EACH term by 16]

L-16 =0.02 x 16

L = 0.02x16 +16


To justify the answer , plug in the value of L in the original equation ,

:)

 

[Mark44]

I am starting to confuse myself here!

The equation is -2.6 = 1/1.5 ln(L/Lo -1)

multiply both sides by 1.5

-2.6x1.5 = ln(L/16 -1)

-3.9= ln(L/16-1)

L/16-1 e^-39

The step above is missing the =, and the step below is wrong. When you multiply both sides of the equation by 16, you need to multiply each term on the left side by 16. IOW, you have to distribute the 16 across both terms.

L/16 -1 = 0.02

L-1 =0.02 x 16

L = 0.02x16 +1
L= 1.32. I know i am going wrong somewhere because my answer does not plug into the original equation?

 

[brenfox]

Thanks Maged, Mark. 16.32 plugs in correctly.