This lecture covers the properties of logarithms. The first property you'll learn about is the product property. We can use this property to break the log apart, or to write two logarithms as a single log. The second property is the quotient property, which is very similar to the first one, and the third property is the power property, which allows us to move the exponent to the front. It is important to use these properties to solve logarithmic equations. To solve a logarithmic equation, first use the properties to combine logs on each side of the equation to get an equation of the form log x = log y. Then equate x and y.
Since both logs on the left and right side of the equation have the same base, we can continue without the logs.
x(x + 36) = 76
x2 + 36x = 76
x2 + 36x − 76 = 0
Factor x2 + 36x − 76 = 0
(x + 38)(x − 2) = 0
Solve using the Zero Product Property
x = − 38
x = 2
By inspection, you can see that x = − 38 is an erroneous solutions to log2x + log2(x + 36) = log276
since ther will be a negative inside the first term. Since that can't happen, the only solution is x = 2
*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
Properties of Logarithms
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.