Use the product property of logarithms, logb(x)+logb(y)=logb(xy).
For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.
Solve for a.
Subtract a from both sides of the equation.
Factor a out of ab-a.
Factor a out of ab.
Factor a out of -a.
Factor a out of a(b)+a⋅-1.
Divide each term by b-1 and simplify.
Divide each term in a(b-1)=b by b-1.
Cancel the common factor of b-1.
Cancel the common factor.
Divide a by 1.
Solve for a natural log of a+ natural log of b = natural log of a+b