ln(A)=ln(C)-kt

Rewrite the equation as ln(C)-kt=ln(A).

ln(C)-kt=ln(A)

Move all the terms containing a logarithm to the left side of the equation.

ln(C)-ln(A)=kt

Use the quotient property of logarithms, logb(x)-logb(y)=logb(xy).

ln(CA)=kt

Since t is on the right side of the equation, switch the sides so it is on the left side of the equation.

kt=ln(CA)

Divide each term in kt=ln(CA) by k.

ktk=ln(CA)k

Cancel the common factor of k.

Cancel the common factor.

ktk=ln(CA)k

Divide t by 1.

t=ln(CA)k

t=ln(CA)k

t=ln(CA)k

Solve for t natural log of A = natural log of C-kt