(Q14.) Sample 3 GCC Math 101/120 Common Final Intermediate Algebra

TL;DR

Learn how to solve equations with logarithms by condensing the logs, changing to exponent form, and factoring.

Transcript

for question number 14 we are going to solve an equation with log here we have log base 6 of x + 1 plus log base 6 of 2x + 1 is equal to 2 whenever we are trying to solve a equation with logs we have to first make sure to combine all the logs together into just one single log and here we have two logs and they're adding and the way to condense addi... Read More

Key Insights

• 🧑‍💻 Combining logs requires condensing addition into multiplication.
• 💁 Changing log equations to exponent form helps in solving for the variable.
• ✋ Factoring is a useful technique for solving higher degree equations.
• 🧑‍💻 Checking the solutions in log equations is necessary to ensure validity.

Questions & Answers

Q: How do you solve equations with logarithms?

To solve equations with logarithms, combine all the logs into one and change the equation to exponent form. Then solve the equation either by factoring or using other algebraic techniques.

Q: How do you condense addition of logs?

To condense addition of logs, write all the terms inside a big parenthesis and multiply them together. This condenses the addition into multiplication.

Q: Why do we change log equations to exponent form?

We change log equations to exponent form to get rid of the log. By raising the base to the exponent on both sides, the log and the base cancel out.

Q: Why is it important to check our answers in log equations?

It is important to check the answers in log equations because negative numbers cannot be inside the log. If a solution gives a negative number inside the log, it is not a valid answer.

Summary & Key Takeaways

• To solve equations with logarithms, combine all logs into one by condensing addition into multiplication.

• Change the equation to exponent form by writing the base of the log as the base of the exponent.

• Solve the equation by factoring and setting each factor equal to zero.