SOLUTION: e^-t/4.6=1.73^2.7t

Question 268917: e^-t/4.6=1.73^2.7t
Answer by persian52(161) (Show Source): You can put this solution on YOUR website!
(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)
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