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...)
(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 n^{x}
= a. then logarithm of a, with n as the base, is x
and it is expressed as log_{n}a=x More common are the
logarithm (base 10), the natural logarithm (base e), and the binary logarithm (base 2). Note:
• if x^{0}= 1, then log_{x}1 = 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 = log_{a}x, then a^{y}=
x (base is a) and viceversa.
For example, when you solve for x in the equation Ln(x) =8, it
yields x = e^{8} and the approximate answer is 2,980.95798705.
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