Solving Exponential Equations

TL;DR

Use logarithms to solve equations with exponential terms by taking the logarithm of both sides.

Transcript

solve 6 to the x power is equal to 45 and give x to the nearest hundredth so we have 6 to the x power is equal to is equal to 45. so to solve this i'm going to take the logarithm of both sides of this equation and there's multiple different bases i could do but i'm going to take the log base 10 of both sides of this equation and the reason i'm goin... Read More

Key Insights

• 🙃 Logarithms can be used to solve exponential equations by taking the logarithm of both sides.
• 😄 The logarithm base 10 is commonly used for ease of calculation on calculators.
• 👻 The change of base formula allows for the conversion of exponential equations to different bases, simplifying the solution process.
• 🙃 Dividing both sides of the equation by the logarithm of the base allows for the isolation of the variable.
• 🤨 The solution can be verified by using the exponential function to raise the base to the calculated value of x.
• 🛝 Precision in rounding affects the closeness of the calculated solution to the actual value.
• ⚾ The change of base formula is a useful tool in solving exponential equations.

Questions & Answers

Q: How can logarithms be used to solve equations with exponential terms?

Logarithms can be used to solve equations with exponential terms by taking the logarithm of both sides. This allows us to manipulate the equation and isolate the variable.

Q: Why did the presenter choose to use the logarithm base 10?

The presenter chose to use the logarithm base 10 because it is easily calculable on most calculators. The logarithm base 10 function allows for accurate calculations without complex manual calculations.

Q: How does the change of base formula relate to solving exponential equations?

The change of base formula allows us to solve exponential equations by converting the equation to a different base. This allows for easier calculations and simplification of the equation, ultimately leading to finding the solution for the variable.

Q: What is the significance of dividing both sides of the equation by the logarithm of 6?

Dividing both sides of the equation by the logarithm of 6 allows us to isolate the variable, x. By simplifying the equation, we can find the numerical value of x.

Summary & Key Takeaways

• To solve the equation 6 to the power of x equals 45, take the logarithm of both sides.

• By using the logarithm properties, simplify the equation to find x.

• The change of base formula can be used to solve exponential equations and verify the solution.