Can a logarithmic equation have a negative solution?
Logarithms cannot have non-positive arguments (that is, arguments which are negative or zero), but quadratics and other equations can have negative solutions. Each log in the equation had the same base, and each side of the log equation ended up with the value, so the solution “checks”.
Why are there extraneous solutions?
The reason extraneous solutions exist is because some operations produce ‘extra’ answers, and sometimes, these operations are a part of the path to solving the problem. When we get these ‘extra’ answers, they usually don’t work when we try to plug them back into the original problem.
When solving a logarithmic equation it is not possible to have solutions that are negative?
Your friend states that a logarithmic equation cannot have a negative solution because logarithmic functions are not defined for negative numbers.
What is the natural logarithmic function of 0?
What is the natural logarithm of zero? ln(0) = ? The real natural logarithm function ln(x) is defined only for x>0. So the natural logarithm of zero is undefined.
Can a logarithmic equation have more than one extraneous solution?
A logarithmic equation can have at most one extraneous solution.
How do you know if a solution is extraneous or extraneous?
To determine if a solution is extraneous, we simply plug the solution into the original equation. If it makes a true statement, then it is not an…
How do you know if it’s an extraneous solution?
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. Example 1: Solve for x , 1x − 2+1x + 2=4(x − 2)(x + 2) .
Why does log (- 1 have no solution?
The log function is used to undo raising something to a power. Just log() has a default base value of 10. or, if we take log(100), we get 2 because 10^2 = 100. So, if you think, “what power does 10 have to be raised to, to get -1”, you will get nothing.
Can logarithms cancel out?
Remember, a logarithm tells you what the exponent is. So log 100 really means “10 to what power is equal to 100?” We know 10 to the 2nd power is 100, so the logarithm is equal to 2. If you had a logarithm with base 3 on one side and a logarithm with base 7 on the other side, they won’t cancel out.
How do you simplify logs on both sides?
To rid an equation of logarithms, raise both sides to the same exponent as the base of the logarithms. In equations with mixed terms, collect all the logarithms on one side and simplify first.
Is ln infinity infinity?
The answer is ∞ . The natural log function is strictly increasing, therefore it is always growing albeit slowly. The derivative is y’=1x so it is never 0 and always positive.
Does the ln of 0 exist?
What is the natural logarithm of zero? The real natural logarithm function ln(x) is defined only for x>0. So the natural logarithm of zero is undefined.
When can you apply the 1 1 property of logarithms to solve an equation?
The one-to-one property can be used if both sides of the equation can be rewritten as a single logarithm with the same base. If so, the arguments can be set equal to each other, and the resulting equation can be solved algebraically.
How do you simplify logarithmic equations?
To solve this type of equations, here are the steps:
- Simplify the logarithmic equations by applying the appropriate laws of logarithms.
- Rewrite the logarithmic equation in exponential form.
- Now simplify the exponent and solve for the variable.
- Verify your answer by substituting it back in the logarithmic equation.
What is an extraneous solution to an equation?
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.
Which is the best description of an extraneous solution?
An extraneous solution is one that arises in a solution of equations, but which on closer inspection is not a solution to the original equation.
