Podcast
Questions and Answers
What can be concluded if the equation is structured as $5^x = 5^3$?
What can be concluded if the equation is structured as $5^x = 5^3$?
- $x = 8$
- $x = 5$
- $x = 3$ (correct)
- $x = 0$
Which method is appropriate for solving the equation $2^x = 3^x$?
Which method is appropriate for solving the equation $2^x = 3^x$?
- Setting x equal to 0
- Using logarithms to isolate the exponent (correct)
- Factoring both sides
- Equating the bases directly
What is the first step to solve the equation $4^x = 16$?
What is the first step to solve the equation $4^x = 16$?
- Express 16 as $4^2$ (correct)
- Isolate x by dividing both sides by 4
- Check for extraneous solutions
- Raise both sides to the power of x
After solving an exponential equation, why is it necessary to check for extraneous solutions?
After solving an exponential equation, why is it necessary to check for extraneous solutions?
If you have the equation $e^{2x} = e^{3x - 1}$, what is the next step after applying logarithms?
If you have the equation $e^{2x} = e^{3x - 1}$, what is the next step after applying logarithms?
What can be inferred about the solution of the equation $7^x = 7^5$?
What can be inferred about the solution of the equation $7^x = 7^5$?
If an exponential equation cannot be simplified to have the same base, which method should be used?
If an exponential equation cannot be simplified to have the same base, which method should be used?
In the process of solving $10^{2x} = 1000$, what is the first step taken?
In the process of solving $10^{2x} = 1000$, what is the first step taken?
When solving the equation $3^x = 27$, what should you do after confirming that both sides can be expressed with the same base?
When solving the equation $3^x = 27$, what should you do after confirming that both sides can be expressed with the same base?
What step is necessary after finding a solution to an exponential equation?
What step is necessary after finding a solution to an exponential equation?
Which statement about the equation $a^x = a^y$ is true given that $a > 0$ and $a \neq 1$?
Which statement about the equation $a^x = a^y$ is true given that $a > 0$ and $a \neq 1$?
When the equation is written as $4^x = 64$, what is the next suitable step?
When the equation is written as $4^x = 64$, what is the next suitable step?
If both sides of an exponential equation cannot be expressed with the same base, what is the primary strategy to use?
If both sides of an exponential equation cannot be expressed with the same base, what is the primary strategy to use?
Which of the following correctly describes extraneous solutions?
Which of the following correctly describes extraneous solutions?
What should be done after finding a solution to the equation $2^x = 8$?
What should be done after finding a solution to the equation $2^x = 8$?
