Can logarithmic equations have extraneous solutions?

Extraneous solutions can occur when solving logarithmic equations, so be careful! The problem typically arises when properties of logarithms are used to combine two or more logarithmic terms into a single term, as discussed next.

Can a logarithmic equation have a negative solution that is not extraneous?

Logarithms cannot have non-positive arguments (that is, arguments which are negative or zero), but quadratics and other equations can have negative solutions.

Can exponential equations have extraneous solutions?

Solve a Logarithmic Equation by Exponentiating Both Sides Simplify the expressions on each side of the equation. Solve the resulting equation. Check your solution, it is possible to get extraneous solutions.

How do you identify extraneous solutions?

To find whether your solutions are extraneous or not, you need to plug each of them back in to your given equation and see if they work. It’s a very annoying process sometimes, but if employed properly can save you much grief on tests or quizzes.

Why do extraneous solutions occur?

​Extraneous Solutions occur because squaring both sides of a square root equation results in 2 solutions (the positive and negative number). Therefore, one of those numbers will be an extraneous solution, or an extra solution which does not fulfill the original equation.

Can a log have a negative solution?

1. You can’t take the logarithm of a negative number or of zero. 2. The logarithm of a positive number may be negative or zero.

Which of the solutions are extraneous?

Extraneous solutions are values that we get when solving equations that aren’t really solutions to the equation.

When should you check for extraneous solutions?

You only need to worry about the extraneous root in the case of a quadratic equation if you made the equation quadratic by multiplying by a variable. Any time you square a negative number or a variable (which may be negative), you risk losing information by making it positive.

Is an extraneous solution a solution?

In mathematics, an extraneous solution (or spurious solution) is a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem.

What is an extraneous solution of an equation?

An extraneous solution is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original equation.

When output of log is negative and positive?

For log(x), x being any number, log(x)=0 if x=1. For values less than 1, it gives negative. Example, log(100) taking base 10 is 2. This is positive.

How do you solve the natural logarithms maze?

Natural Logarithms Equations Maze Directions: Find the solution to each equation to “find the log” and solve the maze. SHOW YOUR WORK! © 2016 Flamingo MathTM(Jean Adams) START: lnë= 6 ln+ln3 = 4 lnë−2= 14ë−2= 5

What is an extraneous solution in math?

In case you are not familiar with the concept, an extraneous solution (also called an extraneous root) is a solution you get in the process of solving, that turns out not to be a solution of the original equation. It is not actually a solution, and is not inherent in the problem itself, but is introduced by what you do.

Why is the negative value of a logarithmic equation extraneous?

But because of the domain of the log, the negative solution is extraneous: is true, but is not. The issue here is that condensing a logarithmic expression (or some other types of expression) can change the domain. For more on this, see Are Properties of Logarithms Missing Something? How can you recognize extraneous solutions?

How do you solve logarithmic equations with substitute solutions?

Remember to always substitute the possible solutions back to the original log equation. x = – 2 x = −2 if they will be valid solutions. Substitute back into the original logarithmic equation and verify if it yields a true statement. x = 5 x = 5 is definitely a solution. However, x =-2 x = −2 as part of our solution.