Solving Exponential Equations With Different Bases Using Logarithms - Algebra

TL;DR

Learn how to solve equations with exponents by taking the logarithm of both sides and manipulating the equation algebraically.

Transcript

have you ever wondered how to solve for x when it's an exponent i mean let's say if you have three plus x equals five this would be easy you know you would subtract both sides by three these two cancel x equals two life is great but how do you solve for that well if you have a calculator it's going to be real fast you ready type in log 5 divided by... Read More

Key Insights

• 🙃 Taking the logarithm of both sides of an equation with exponents allows you to manipulate and solve the equation algebraically.
• ❓ Moving the exponent to the front is a property of logarithms and is a useful step in solving equations with exponents.
• ⚾ In some cases, using the common base of the numbers in the equation can simplify the problem without the need for logarithms.

Questions & Answers

Q: How do you solve equations with exponents using logarithms?

To solve for x when x is an exponent, take the logarithm of both sides of the equation. Then, use algebraic manipulation to isolate x.

Q: Can you explain the steps involved in solving equations with exponents using logarithms?

Step 1: Take the logarithm of both sides. Step 2: Move the exponent to the front using the properties of logarithms. Step 3: Solve for x by isolating it on one side of the equation.

Q: Are there cases where you can solve equations with exponents without using logarithms?

Yes, if the numbers in the equation have a common base, you can simplify the problem by using the properties of exponents without resorting to logarithms.

Q: How do you check whether the solution is correct?

You can check your solution by substituting the value of x back into the original equation and verifying that both sides of the equation are equal.

Summary & Key Takeaways

• To solve for x when x is an exponent, take the logarithm of both sides of the equation.

• Move the exponent to the front using the properties of logarithms.

• Solve for x by isolating it on one side of the equation.

• In some cases, the common base of the numbers in the equation can be used to simplify the problem without using logs.