# Rewrite Expression Using Change Of Base Formula Worksheet

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The change of base formula lets us rewrite a logarithm from one base to another. It's done using the formula: \log_b M = \frac{\log_c M}{\log_c b}, where $$b$$, $$M$$, and $$c$$ are positive numbers (not 1). This is useful for converting logarithms, especially when using common logarithms (base 10) for easier calculations and applications in various fields.
Example: Rewrite $$\log_3 8$$ using base 2 logarithms.

Algebra 2
Logarithms

## How Will This Worksheet on "Rewrite Expression Using Change of Base Formula" Benefit Your Student's Learning?

• It helps manage logarithms in different types of math problems and situations.
• Simplifies logarithmic expressions by changing them to a base that's easier to handle.
• Improves skills in handling algebra and understanding how logarithms behave.
• Helps accurately calculate and analyze growth, decay, and other logarithmic functions in math and science.

## How to Rewrite Expression Using Change of Base Formula?

• Start with the given logarithmic expression in a specific base, such as $$\log_b M$$.
• Use the formula \log_b M = \frac{\log_c M}{\log_c b}, where $$c$$ can be any base different from $$b$$.
• Select $$c$$ as a base convenient for the calculation or context, often base 10 (common logarithms) or base 2 (binary logarithms).
• Substitute the values of $$b$$, $$M$$, and $$c$$ into the formula and simplify if necessary, ensuring the expression of the result clearly in terms of the new base $$c$$.

## Solved Example

Q. Rewrite as a quotient of two common logarithms. Write your answer in simplest form. $\log_3 33 =$
Solution:
1. Apply change of base formula:$\log_b a = \frac{\log_c a}{\log_c b}$$\newline$ Use the change of base formula for logarithms.$\newline$Let's take base of $10$. $\log_{3} 33 = \frac{\log_{10}(33)}{\log_{10}(3)}$
2. Simplify the expression: Simplify the expression.$\newline$ $\log_{3} 33 = \frac{\log_{10}(33)}{\log_{10}(3)}$

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