Change of base formula | Logarithms | Algebra II | Khan Academy

TL;DR

The change of base formula allows you to find logarithms with bases that your calculator doesn't support.

Transcript

Use the change of base formula to find log base 5 of 100 to the nearest thousandth. So the change of base formula is a useful formula, especially when you're going to use a calculator, because most calculators don't allow you to arbitrarily change the base of your logarithm. They have functions for log base e, which is a natural logarithm, and log ... Read More

Key Insights

• 💦 The change of base formula is useful when working with logarithms that have bases not supported by calculators.
• ⚾ Logarithms without a specified base usually imply base 10 or base e (natural logarithm).
• 👻 Converting logarithms to bases like 10 or e allows for easier calculations on calculators.
• 👍 The change of base formula can be proven using exponential and logarithmic properties.
• ✊ Verifying the change of base formula involves checking if the obtained result matches the original value or if raising the base to the derived power gives the original value.
• 💦 Log base 10 is commonly used and understood when working with logarithms, and it is supported by most calculators.
• 💦 The change of base formula provides a way to switch between different bases while working with logarithms.

Questions & Answers

Q: Why is the change of base formula useful?

The change of base formula is useful because it allows us to calculate logarithms with bases that are not supported by most calculators. By converting the base using the formula, we can work with bases like 10 or e (natural logarithm).

Q: What does log without any other information imply?

When someone writes log without specifying the base, it usually implies log base 10. This is the default base assumption, unless a different base is explicitly mentioned.

Q: How can the change of base formula be used to find logarithms on a calculator?

By using the change of base formula, you can convert a logarithm with a desired base to a logarithm with a base supported by the calculator, such as base 10. This allows you to use the calculator's log function and obtain the desired result.

Q: How can the change of base formula be verified?

The change of base formula can be verified by evaluating the logarithm with the base obtained using the formula. If the result matches the original value, then the formula is correct. It can also be verified by raising the base to the power obtained from the formula and checking if it equals the original value.

Summary & Key Takeaways

• The change of base formula allows you to convert a logarithm with a specific base to a logarithm with a different base.

• Most calculators only have functions for logarithms with base 10 or base e (natural logarithm), so the change of base formula is useful in those cases.

• To find log base 5 of 100, you can use the change of base formula and convert it to log base 10 of 100 divided by log base 10 of 5.