Solve log_2(x - 5) + log_2(x - 3) - log_2(x) = 3 Equation with Three Logarithms MyMathlab

TL;DR

Solving a complex logarithmic equation step by step.

Transcript

in this problem we have three logarithms and we have to solve for X so we have log base two of X minus five plus log base two of X minus three minus log base two of X and that's equal to three so whenever you have two or more logs in this case three you want to combine all of these logs into one so you can exponentiate so first we'll use the produc... Read More

Key Insights

• ▶️ Combining logarithms simplifies the equation before moving forward.
• ❓ Exponentiation is used to eliminate the logarithms in the equation.
• 🤩 Factoring the resulting quadratic equation plays a key role in finding the solutions.

Questions & Answers

Q: How do you start solving a logarithmic equation with multiple logarithms?

Begin by combining the logarithms using logarithmic rules, based on whether they are added or subtracted, and simplify the equation before proceeding.

Q: Why is it important to remove the logarithms by exponentiation in the process?

Exponentiation helps eliminate the logarithms and convert the equation into a more manageable algebraic form to solve for the variable effectively.

Q: What is the significance of factoring the resulting quadratic equation?

Factoring the quadratic equation is crucial as it helps identify the potential solutions for the variable by breaking down the equation into its factors.

Q: Why is it necessary to check the obtained solutions in a logarithmic equation?

Checking the solutions ensures that they are valid and do not lead to undefined or incorrect results due to the nature of logarithmic functions.

Summary & Key Takeaways

• Given a logarithmic equation with multiple logarithms, the approach involves combining them using logarithmic rules.

• After simplifying the equation, the logarithms are removed by exponentiation to solve for the variable.

• The process continues with factoring the resulting quadratic equation and checking the potential solutions to find the correct answer.