6=[(84)/(1+7e^(-x))]. six is equal to 84 over 1 + 7e, the e raised to the -x. Thanks to whoever tries!
multiply both sides by 1+7e^-x to get
6*(1+7e^-x) = 84
divide by 6
1+7e^-x = 84/6 = 14
subtract 1
7e^-x = 13
divide by 7
e^-x = 13/7
natural log of both sides
ln(e^-x) = ln(13/7)
remember ln (e^x) = x
so, -x = ln(13/7)
x = -ln13/7
also remember -ln y = ln (1/y)
so x = ln (7/13)
6=[(84)/(1+7e^(-x))]
OK, first thing is first. You have to get rid of the denominator.
Multiply both sides by 1+7e^-x
6(1+7e^-x) = 84
Distribute the 6
6+42e^-x = 84
Subtract the 6
42e^-x = 72
Divide by 42
e^-x = 72/42 = 13/7
Use the reciprocal of e to eliminate the negative exponent
1/e^x = 13/7
Multiply both sides by e^x
1 = 13/7e^x
Divide both sides by 13/7
7/13 = e^x
Time to go logging
ln(7/13) = ln(e^x)
Bring the x down front
ln(7/13) = x(ln)e
ln(e) cancels
ln(7/13) = x
-----------------
>.<
That was a doozie. =D
Comments
multiply both sides by 1+7e^-x to get
6*(1+7e^-x) = 84
divide by 6
1+7e^-x = 84/6 = 14
subtract 1
7e^-x = 13
divide by 7
e^-x = 13/7
natural log of both sides
ln(e^-x) = ln(13/7)
remember ln (e^x) = x
so, -x = ln(13/7)
x = -ln13/7
also remember -ln y = ln (1/y)
so x = ln (7/13)
6=[(84)/(1+7e^(-x))]
OK, first thing is first. You have to get rid of the denominator.
Multiply both sides by 1+7e^-x
6(1+7e^-x) = 84
Distribute the 6
6+42e^-x = 84
Subtract the 6
42e^-x = 72
Divide by 42
e^-x = 72/42 = 13/7
Use the reciprocal of e to eliminate the negative exponent
1/e^x = 13/7
Multiply both sides by e^x
1 = 13/7e^x
Divide both sides by 13/7
7/13 = e^x
Time to go logging
ln(7/13) = ln(e^x)
Bring the x down front
ln(7/13) = x(ln)e
ln(e) cancels
ln(7/13) = x
-----------------
>.<
That was a doozie. =D