Math Help Please! Calculus - May be a log problem? It has been so long!?

Question

So... I am taking a radiology class and we are getting reintroduced to some math, it has been years since I have taken a math class...I got through 99.9% of it and now I am on the last problem and have no idea! Please walk me through it!
Also please tell me what kind of problem it is so I can look it up and re-learn these!

SOLVE FOR M: 300 = 600e^-2M
(-2M being the exponent on the e)

Thanks !!!

Answer 1

This is a problem about the exponential function--it will probably be covered in a calculus or algebra text under a section called "exponential functions." To solve the problem:

300 = 600e^(-2M)

First, divide by 600, to isolate the exponential part:

1/2 = e^(-2M)

Now, take the natural logarithm of both sides:

ln (1/2) = ln (e^(-2M))

But ln and e^ are inverse functions, so they cancel, and we are left with

ln (1/2) = -2M

Now divide by -2, which gives the answer

ln (1/2) / -2 = M.

This gives M a value of approximately 0.346.

Answer 2

This is a log problem. It also looks like a half- life problem.
To solve for M:
1), Divide by 600:
1/2 = e^(-2M) = 1/e^(2M)
2). Invert both sides:
e^2M = 2
3), Take the log of both sides and solve,
remembering that ln(e^x) = x.
2M = ln 2
M = ln 2/2 = 0.346(approx.).

Answer 3

Natural logs it is...

300 = 600e^-2M
1/2 = e^-2M
ln(2^-1) = ln(e^-2M)
ln(2^-1) = -2M
-ln(2) = -2M
(1/2)ln(2) = M

Answer 4

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Answer 5

300 = 600e^(-2M)
ln 300 = ln 600 + (-2M)ln e *
ln 300 - ln 600 = -2M
ln 600 - ln 300 = 2M
ln (600/300) = 2M **
ln 2 = 2M
M = (ln 2)/2

notes:

* ln e = 1
** ln m - ln n = lm(m/n)

Try searching for topics in logarithmics and natural logarithms.

Answer 6

log problem

300 = 600e^-2M
=> ln300 = ln 600e^-2M
=> ln300 = ln 600 + lne^-2M
=> ln300 = ln 600-2M lne.... ...... lne = 1
=> 2M = ln 600 - ln 300
=> 2M = ln (600/300)
=> M = (ln2) /2
=> M = 0.3465....

QED

Answer 7

300 = 600 e^(-2M)

300/600 = e^(-2M)

e^(-2M) = 1/2 = 2^(-1)

ln (e^(-2M)) = ln(2^(-1))

-2M = (-1) ln(2)

M = ln(2)/2

Hope this helps. =)

Answer 8

1/2 = e^-2M
ln(1/2) = ln(e^-2M)
ln(1/2) = -2Mln(e)
ln(1/2)/-2 = M

log problem

Answer 9

log problem