Solving exponential equations using exponent properties (advanced) | High School Math | Khan Academy

TL;DR

This video demonstrates how to solve exponential equations, using common bases and simplifying expressions.

Transcript

• [Voiceover] So, let's get even more practice solving some exponential equations, and I have two different exponential equations here. And like always, pause the video and see if you can solve for x in both of them. All right, let's tackle this one in purple first. And you might first notice that on both sides of the equation I have different base... Read More

Key Insights

• 👻 Rewriting exponential equations using common bases simplifies the equation and allows us to solve for x.
• 😑 Multiplying exponents together is a helpful rule when simplifying exponential expressions.
• 🤘 Distributing the negative sign to each term in the parenthesis is necessary when subtracting exponents.

Questions & Answers

Q: How does finding a common base help in solving exponential equations?

Finding a common base allows us to rewrite the equation in terms of powers of that common base, making it easier to simplify and solve for x.

Q: What is the rule for multiplying exponents?

When we have an exponential expression raised to another power, we can multiply the exponents together. This simplifies the equation and allows us to set the exponents equal to each other.

Q: In the second example, why did the exponent on the left-hand side become 4-x plus 3 minus 18 minus 2-x?

To subtract the exponents on the right-hand side from the exponents on the left-hand side, we need to apply the properties of exponents and distribute the negative sign to each term in the parenthesis.

Q: Why did we subtract 5 from both sides in the second example?

By subtracting 5 from both sides, we isolate the variable x on one side of the equation and simplify it to find the solution.

Summary & Key Takeaways

• The video discusses how to solve exponential equations by finding common bases and simplifying expressions.

• The first example involves rewriting the equation using powers of two and then solving for x.

• The second example demonstrates rewriting the equation using the same bases and then solving for x.