ln [5.01E-3] = ln(4.86E-2) - (1.80E-2s-1)(t s) Solve for t.
t = 126 s
First I did 4.86e-2 - 1.80e-2 and then on my calculator I pressed the 2nd button and then ln and got 1.031. Then I did the same thing to get the ln of 5.01e-3 and divided that by 1.031 but did not get 126 as the answer. Where did I mess up?
Math - Steve, Thursday, March 8, 2012 at 5:31pm
Does the equation mean
ln(.00501) = ln(.0486) - (.0180s - 1)(ts)?
Doesn't look like that's what you were doing. Try reposting with plenty of parentheses for clarity.
Use ^ for power if needed as in s^(-1) for 1/s
yes that's what it means and how I posted it is exactly how it is written on my homework but I just cant seem to get that answer
Am I suppose to convert seconds into something else??
ln .0051 = −5.2963
ln .0486 = −3.0241
so now we have
-2.2722 = .0180t(s-s^2)
t = 126.233/(s-s^2)
Now, if the problem read
ln [5.01E-3] = ln(4.86E-2) - (1.80E-2/s)(t)
it would be a better fit.
I think your s-1 was really s^(-1)
ok thank you so much!!!
To solve for t in the equation ln [5.01E-3] = ln(4.86E-2) - (1.80E-2s-1)(t s), you need to follow these steps:
1. Start by subtracting ln(4.86E-2) from both sides of the equation:
ln [5.01E-3] - ln(4.86E-2) = - (1.80E-2s-1)(t s)
2. Use the logarithmic property that ln(x) - ln(y) = ln(x/y) to simplify the equation:
ln [5.01E-3 / 4.86E-2] = - (1.80E-2s-1)(t s)
3. Simplify the logarithm on the left side of the equation:
ln (5.01E-3 / 4.86E-2) = - (1.80E-2s-1)(t s)
4. Take the natural logarithm (ln) of both sides of the equation:
ln [ ln (5.01E-3 / 4.86E-2) ] = ln [ - (1.80E-2s-1)(t s) ]
5. Divide both sides of the equation by - (1.80E-2s-1):
ln [ ln (5.01E-3 / 4.86E-2) ] / - (1.80E-2s-1) = t s
6. Finally, calculate the value of t by evaluating the expression on the left side of the equation using a calculator:
t ≈ ln [ ln (5.01E-3 / 4.86E-2) ] / - (1.80E-2s-1)
Given the provided values of ln(5.01E-3 / 4.86E-2) ≈ -1.031 and (1.80E-2s-1) = 1.80E-2, you can substitute these values into the equation:
t ≈ (-1.031) / - (1.80E-2s-1)
Follow the calculations as shown below:
t ≈ (-1.031) / - (1.80E-2)
t ≈ 57.28
Therefore, the approximate value of t is 57.28 seconds, not 126 seconds as previously mentioned.