In Algebra II, you will have to solve many equations containing logarithms. Logarithms are mathematical expressions that can be converted into exponential expressions: if log(base b)(x)=a, then b^a=x. You often will see the natural logarithm, ln x, in math problems; ln x can be written as log(base e)(x), in which e is approximately equal to 2.718. When working with logarithms, you will find the possibility of converting them into exponential expressions to be invaluable. This conversion often is the key to getting rid of the logarithm and solving the equation.
Isolate the expression containing the logarithm, so that it is on one side of the equation only. If your expression is ln(x-3)-2=6, add 2 to both sides of the equation to obtain ln(x-3)=8.
Take the exponential of both sides of the equation, to obtain e^(ln(x-3))=ln 8.
Simplify both sides of the equation. You can simplify the left side of the equation by using the property of natural logarithms that e^(ln x) equals x. Therefore, the left side simplifies to x-3, while the right side simplifies to 2.08.
Solve the equation the way you would traditionally solve algebraic equations. Since the equation now is x-3=2.08, add 3 to both sides of the equation to obtain x=5.08.