solve the following equation for t and please show all steps

solve the following equation for t and please show all steps. 10 = 40 (e-0.0693 x t)

Solution:

10 = 40 e^-0.0693*t

divide by 40 on both side

1/4 = e^0.0693*t

take log on both side

ln(1/4) = ln( e^0.0693*t )

Apply log rule

log A ^B = B log A

-0.0693*t = ln(1/4)

-0.0693*t = ln(1) - ln (4) ( log(A/B) = logA -logB )

-0.0693*t = - ln (4)

-0.0693*t = - ln (2²)

t = 2ln2 / (0.0693)

t = 20.0042 ( Approx. )

Answer