Algebra II: Solving Logarithmic Equations
 This is a free lesson from our course in Algebra II

 In this lesson you'll take a look at how to solve a logarithmic equation, rewriting it in exponential form and solving for the variable. You will find some examples with solution, and the instructor explains all that with the help of audio, video presentation and in own hand writing. Logarithmic equations contain logarithmic expressions and constants. When one side of the equation contains a single logarithm and the other side contains a constant, the equation can be solved by rewriting the equation as an equivalent exponential equation using the definition of logarithm. All solutions of logarithmic equations must be checked, because negative numbers do not have logarithms. (More text below video...)
Other useful lessons:
 Evaluate value of a logarithmic expression The laws of logarithm Solving assorted equations using logarithms Natural logarithm Convert logarithmic expression from one base to another Is logarithmic statement sometimes, always or never true
(Continued from above) Solving logarithmic equations usually requires using properties of logarithms. The reason you usually need to apply these properties is so that you will have a single logarithmic expression on one or both sides of the equation. Once you have used properties of logarithms to condense any log expressions in the equation, you can solve the problem by changing the logarithmic equation into an exponential equation and solving.
It is illustrated that if nx = a. then logarithm of a, with n as the base, is x and it is expressed as logna=x More common are the logarithm (base 10), the natural logarithm (base e), and the binary logarithm (base 2).
Note:
• if x0= 1, then logx1 = 0, means log 1 is always zero for any base and you can't take log of any number less than 1.
• if y = ln x, then ey = x (base is e) and if y = logax, then ay= x (base is a) and vice-versa.
For example, when you solve for x in the equation Ln(x) =8, it yields x = e8 and the approximate answer is 2,980.95798705.
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