The discussion revolves around solving the equation w = 1/h ln(l/lo - 1) with given values w = -2.6, lo = 16, and h = 1.5 to find L. The correct approach involves isolating the logarithmic term and applying the exponential function to solve for L. The final correct value for L is determined to be approximately 16.32, which satisfies the original equation. Participants emphasize the importance of correctly applying mathematical operations and checking each step to avoid errors.
PREREQUISITESStudents studying mathematics, particularly those focusing on algebra and logarithmic equations, as well as educators seeking to clarify concepts related to logarithmic functions and their applications in problem-solving.
Do this one step at a timeL/16-1 = e^-0.256
Get L on its own
L = e^-0.256x16+1
Check this step.2.6 = 1/1.5 ln(l/16 - 1)
Make the log term the subject.
ln(L/16 -1) = 1/1.5/-2.6
brenfox said:ln(L/16 -1) = 1/1.5/-2.6
brenfox said:L/16 -1 = e^-0.256
L -1 = e^-0.256 x 16
To make the log term the subject, why not simply multiply (both sides) by 1.5 ?brenfox said:...
2.6 = 1/1.5 ln(l/16 - 1)
Make the log term the subject.
ln(L/16 -1) = 1/1.5/-2.6
...
brenfox said:L/16 -1 = 0.02
L-1 =0.02 x 16
-2.6x1.5 = ln(L/16 -1)brenfox said: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.
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.brenfox said: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
brenfox said: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?