# Convert Logarithmic Equation In Exponential Form Worksheet

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To convert a logarithmic equation to exponential form, identify the base, the argument, and the result. For a logarithmic equation $$\log_a(b) = c$$, convert it to exponential form as $$a^c = b$$. This conversion shows that raising the base $$a$$ to the exponent $$c$$ equals the argument $$b$$. This highlights the inverse relationship between logarithms and exponents. Use this worksheet to enhance your understanding of exponential and logarithmic functions.

Algebra 2
Logarithms

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

• Converting logarithmic equations to exponential form helps students discover unknowns more easily.
• Understanding both forms enables students to see the link between logarithms and exponents.
• Practicing these conversions improves students' skills in handling algebraic equations.
• Converting equations provides another method for solving math problems.
• Knowing how to convert these equations is essential for calculus and higher-level math courses.

## How to Convert Logarithmic Equation in Exponential Form?

• Identify the base, argument, and result in the logarithmic equation.
• Note that the base is the number after "log," the argument is the number inside the logarithm, and the result is what the logarithm equals.
• Convert $$\log_a(b) = c$$ to exponential form $$a^c = b$$.

## Solved Example

Q. Write the logarithmic equation in exponential form.$\newline$$\log_7 373 = 3$
Solution:
1. Identify Values: $\log_2(8) = 3$$\newline$Identify $b$, $x$, and $y$.$\newline$Compare $\log_2(8) = 3$ with $\log_b(x) = y$.$\newline$$b = 2$$\newline$$x = 8$$\newline$$y = 3$
2. Convert to Exponential: $\newline$$\log_2(8) = 3$$\newline$Convert the logarithmic equation to exponential equation.$\newline$Substitute $b = 2$, $x = 8$, and $y = 3$ in $b^y = x$.$\newline$Exponential equation: $2^3 = 8$

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