solving a logarithmic equation with different bases

TL;DR

The video explains how to use the change of base formula for logarithms to solve equations with different bases.

Transcript

okay Jenna this is for you welcome stop this log equation but notice that we do have different bases for the logarithm but it's okay because we have the change of base formula for the logarithm and let me write it down right here for you guys suppose today we have log with space B and then let's say the inputs X right here well this B can be anythi... Read More

Key Insights

• ⚾ The change of base formula allows us to convert logarithms with different bases into a common base, making them easier to work with.
• 🤢 The formula can be written as log X over log B or ln X over ln B, depending on the base we want to use.
• ⚾ The change of base formula is useful when solving equations that involve logarithms with different bases.
• ⚾ The natural logarithm, ln, is commonly used in the change of base formula as it has a base of E.
• ⚾ When using the change of base formula, the top and bottom of the fraction should have the same logarithmic base.
• ❓ The coefficients in front of logarithms can be manipulated to simplify equations.
• 🟰 In equations where logarithms are set equal to each other, the inputs must also be equal due to the one-to-one nature of logarithmic functions.

Questions & Answers

Q: What is the change of base formula for logarithms?

The change of base formula states that log base B of X can be written as log X over log B or ln X over ln B.

Q: Can any base be used in the change of base formula?

Yes, any base can be used as long as it is a positive number and not equal to 1.

Q: Why do we use the change of base formula?

The change of base formula allows us to convert logarithms with different bases into a common base, making them easier to solve.

Q: How can we solve an equation with different base logarithms?

By applying the change of base formula, we can convert the logarithms into a common base and solve the equation using algebraic methods.

Summary & Key Takeaways

• The video introduces the change of base formula for logarithms, which allows us to use logarithms with different bases.

• The formula states that log base B of X can be written as log X over log B or ln X over ln B.

• The video demonstrates how to apply the change of base formula to solve equations with different base logarithms.