The IUSC method for solving logarithmic equations may introduce extraneous solutions. Extraneous solutions are discussed below. Here are examples of logarithmic equations …

You should be convinced that the ONLY valid solution is [latex]\large{\color{blue}x = {1 \over 2}}[/latex] which makes [latex]\large{\color{red}x = -{1 \over 2}}[/latex] an extraneous answer. …

This practice example shows how to solve a logarithmic equation with an extraneous solution. It uses the properties of logarithms to condense the equation in...

Nov 16, 2022 · Here is a set of practice problems to accompany the Solving Logarithm Equations section of the Exponential and Logarithm Functions chapter of the notes for Paul Dawkins …

Dec 24, 2024 · We can start solving \(\log_{6}(x+4) + \log_{6}(3-x) = 1\) by using the Product Rule for Logarithmic Functions to rewrite the equation as \(\log_{6}\left[(x+4)(3-x)\right] = 1\). …

-Check for extraneous solutions. Example 1: Solve the following logarithmic equation. log(𝑥2−𝑥−5)=0 SOLUTION: -Since all logs are contracted, we will start by exponentiating. Since …

Steps for Solving an Equation Involving Logarithmic Functions. Isolate the logarithmic function. (a) If convenient, express both sides as logs with the same base and equate arguments. (b) …

The logarithm function has domain [latex](0,\infty)[/latex] so any solutions must result in all logarithms having positive arguments. A solution that results in an argument that is zero or …

non-solution is called an extraneous solution, and is a good reason to check your answers, so that you do not erroneously give such a solution. Example 18.6. Solve log 2 (x) = log 2 (2x+ 1). …

The equation $\log(x-4) = \log(2x-6)$ provides an example. Extraneous solutions can also result from ignoring physical constraints in applied problems (e.g. length and mass are positive …