Question 268917
(e^(-t))/(4.6)=1.73^(2.7)t

Divide 1 by 4.6 to get 0.22.
0.22e^(-t)=1.73^(2.7)t

Raise 1.73 to the 2.7th power.
0.22e^(-t)=4.39t

Divide each term in the equation by 0.22.
(0.22e^(-t))/(0.22)=(4.39t)/(0.22)

Cancel the common factor of 0.22.
e^(-t)=(4.39t)/(0.22)

Divide 4.39 by 0.22 to get 20.21.
e^(-t)=20.21t

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(e^(-t))=ln(20.21t)

The left-hand side of the equation is equal to the exponent of the logarithm argument because the base of the logarithm equals the base of the argument.
-t=ln(20.21t)

The logarithm of a product is equal to the sum of the logarithms of each factor (e.g. log(xy)=log(x)+log(y)).  The logarithm of a product is equal to the difference of the logarithms of each factor (e.g. log((x)/(y))=log(x)-log(y)).
-t=(ln(20.21)+ln(t))

The natural logarithm of 20.21 is 3.01.
-t=(3.01)+ln(t)

Remove the parentheses around the expression 3.01.
-t=3.01+ln(t)