I need to rearrange the equation to make t the subject P 19

I need to rearrange the equation to make t the subject. P = 19.5e^(0.0163xt) I don\'t know why I have problems doing this. Any assistance would help. Thanks.

Solution

Defininition: a = e ^b. Then , logarithm of a to the base e is equal to b . Or, log y = b.

Log(m*n) =log m+logn ; log (m/n) = log m - log n and log(m^n) = n*log m. We use these below:

Given P=19.5e^(0.0163*t), to find t in terms of P, treating x as multiplication sign.

Taking logarithms with respect to the base e on both sides,

Log P = log(19.5)+0.0163*t.

log P - log (19.5) = 0.0163*t

Divide both sides by 0.0163 :

(log P-log19.5) /0.0163=t .Now, t in the subject form is given as below:

t=(log P - log 19.5)/0.0163 or

t=1/(0.0163)log(P/19.5) or

t=(1/0.0163)(logP-2.970414466)

t=61.34969325 log(P/19.5) or

t=61.34969325log(P)-182.2340163

You can have any of the convenient form of expression for t in terms of P.

NB; If P = 19.5 e^(0.0163xt). If x is a variable, then,

t=1/(0.0163 x)log(P/19.5) or

t=(61.34969325/x) log(P/19.5) etc