# Convert Exponential Equation In Logarithmic Form Worksheet

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To convert an exponential equation to logarithmic form, identify the base, the exponent, and the result. Given an exponential equation of the form $$a^b = c$$, rewrite it in logarithmic form as $$\log_a(c) = b$$. This means that the logarithm of $$c$$ with base $$a$$ is equal to the exponent $$b$$. Logarithms are the inverse operations of exponentiation, expressing the power to which the base must be raised to obtain the given number.

Algebra 2
Logarithms

## How Will This Worksheet on "Convert Exponential Equation in Logarithmic Form" Benefit Your Student's Learning?

• Converting exponential equations to logarithmic form simplifies solving for unknown exponents, making it easier for students to handle complex equations.
• Understanding both exponential and logarithmic forms deepens students' comprehension of the relationship between these concepts.
• This conversion offers alternative problem-solving strategies, enhancing students’ mathematical toolkit.
• Real-world situations, such as population growth and substance decay, use these skills, making this knowledge practical.
• Logarithms are essential in calculus, particularly for working with exponential functions, critical for advanced math courses.

## How to Convert Exponential Equation in Logarithmic Form?

• Identify the base, exponent, and result in the exponential equation.
• Note that the base is the number raised to a power, the exponent is the power, and the result is the operation's outcome.
• Convert the exponential form $$a^b = c$$ to the logarithmic form $$\log_a(c) = b$$.

## Solved Example

Q. Convert the exponential equation in logarithmic form.$\newline$$9^3 = 729$
Solution:
1. Exponential and Logarithmic Forms: Understand the relationship between exponential and logarithmic forms.$\newline$An exponential equation of the form $b^y = x$ can be rewritten in logarithmic form as $\log_b x = y$, where $b$ is the base, $y$ is the exponent, and $x$ is the result.
2. Components of Exponential Equation: Identify the components of the exponential equation.$\newline$In the equation $9^3 = 729$, the base $(b)$ is $9$, the exponent $(y)$ is $3$, and the result $(x)$ is $729$.
3. Conversion to Logarithmic Form: Convert the exponential equation to logarithmic form. $\newline$$b^y = x$ can be rewritten as $\log_b x = y$. $\newline$ $9^3 = 729$ can be rewritten as $\log_9 729 = 3$.

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