iCoachMath
STEM Excellence Series: Empowering the Next Generation
CHANGE OF BASE FORMULA
Change Of Base Formula
Ques: Use the change of base formula to evaluate.
Definition Of Change Of Base Formula
Change of base formula states that: For all positive numbers x, y, and z
where 
and 
Example of Change of Base Formula
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Solved Example onChange of Base Formula
Ques: Use the change of base formula to evaluate. 
Choices:
A. 4.56
B. 4.86
C. 0.21
D. 5.16
Correct Answer: B
Solution:
Step 1:
Quick Summary
- Convert logarithms to a common base for easier calculation.
- Useful for evaluating logarithms on calculators.
- Simplify expressions involving logarithms with different bases.
\[ log_{y}(x) = \frac{log_{z}(x)}{log_{z}(y)} \]
🍎 Teacher Insights
Emphasize the importance of understanding the conditions for the formula. Provide plenty of practice problems with varying bases. Relate it to exponential functions.🎓 Prerequisites
- Logarithms
- Exponents
- Basic Algebra
Check Your Knowledge
Q1: Evaluate log8(16) using the change of base formula.
Q2: Simplify loga(b) / loga(c).
Frequently Asked Questions
Q: Why is the change of base formula useful?
A: It allows you to evaluate logarithms with any base using a calculator that typically only has log base 10 or natural log.
Q: Can I use any base when applying the change of base formula?
A: Yes, as long as the new base is a positive number not equal to 1. Common choices are base 10 or base e (natural logarithm).