Solve the Logarithmic Equation log_4(x + 11) - log_4(x - 4) = 2 MyMathlab

TL;DR

Solving a logarithmic equation step by step with a final answer check.

Transcript

this problem we have two logarithms and we have to solve for X so we have log base 4 of X plus 11 minus log base 4 of X minus 4 and that's equal to 2 it's a pretty cool problem so whenever you have a more than one log you want to combine it and make it one log so we have a minus sign so we can turn this into a fraction so this is the log base 4 of ... Read More

Key Insights

• ❓ Combining logarithms using properties simplifies complex equations.
• ❓ Exponentiation removes logarithms to isolate the variable for solution.
• 🪡 Careful distribution and calculation are needed to find the correct value of the variable.
• 🧑‍💻 Checking the final answer in logarithmic equations with multiple logs is highly recommended.
• ❓ Understanding logarithmic properties is crucial for solving such equations accurately.
• 🖐️ Each step in solving a logarithmic equation plays a crucial role in obtaining the correct solution.
• 🤩 Mathematical precision and attention to detail are key in solving logarithmic equations.

Questions & Answers

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

To solve a logarithmic equation with multiple logs, begin by combining them using the properties of logarithms. For a subtraction in the logs, convert it to division to simplify the equation.

Q: Why is it necessary to exponentiate to remove logarithms in the equation?

Exponentiation is necessary to remove logarithms from the equation because it allows us to isolate the variable X and solve for it. By exponentiating using the base of the logarithms, we can simplify the equation further.

Q: What step follows after simplifying the equation through exponentiation?

After simplifying the equation through exponentiation, the next step involves distributing and solving for the variable X. This process requires careful manipulation of the equation to isolate X and find its value.

Q: Why is it crucial to check the final answer in a logarithmic equation with multiple logs?

Checking the final answer in a logarithmic equation with multiple logs is essential to ensure its validity. In cases where the original equation involves more than one log, errors in calculation can lead to incorrect solutions.

Summary & Key Takeaways

• Given a logarithmic equation involving two logs, the objective is to solve for X.

• Combine the logs using properties of logarithms to simplify the equation.

• Exponentiate to remove the logarithms and solve for X step by step, followed by a crucial answer check.