# Convert Natural Exponential Equation In Logarithmic Form Worksheet

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To convert a natural exponential equation to logarithmic form, identify the base $$e$$, the exponent, and the result. For a natural exponential equation written as $$e^x = y$$, rewrite it in logarithmic form as $$\ln(y) = x$$. This means that the natural logarithm of $$y$$ is equal to $$x$$. This conversion helps in understanding the relationship between the natural exponential function and the natural logarithm, which is the inverse function.

Algebra 2
Logarithms

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

• Converting natural exponential equations to logarithmic form helps students see how exponents and logarithms relate, specifically with the natural base $$e$$.
• This approach offers another way to solve equations involving $$e$$, useful in various math problems.
• Learning this conversion is crucial for advanced math topics like calculus and differential equations.
• It provides additional techniques for solving complex math problems, making students more versatile.
• Properly converting between exponential and logarithmic forms helps students solve math problems accurately and quickly.

## How to Convert Natural Exponential Equation in Logarithmic Form?

• Recognize that the equation involves the natural base $$e$$, written in the form $$e^x = y$$. Here, $$e$$ is the base, $$x$$ is the exponent, and $$y$$ is the result.
• Know that the natural logarithm ($$\ln$$) is the inverse of the natural exponential function. This means the natural logarithm undoes the exponentiation by $$e$$.
• Convert the equation by using the natural logarithm. The result of the exponential equation becomes the argument of the natural logarithm.
• Express the equation as $$\ln(y) = x$$, indicating that the natural logarithm of $$y$$ is equal to $$x$$. This shows the inverse relationship clearly.

## Solved Example

Q. Convert the exponential equation in logarithmic form.$\newline$$e^4 \approx 54.598$
Solution:
1. Identify base, exponent, and result: Identify the base ($b$), the exponent ($y$), and the result ($x$) in the exponential equation $e^4 \approx 54.598$.$\newline$In this case, the base $b$ is $e$ (the base of natural logarithms), the exponent $y$ is $4$, and the result $x$ is approximately $54.598$.
2. Convert to logarithmic form: Convert the exponential equation to logarithmic form.$\newline$The exponential equation $e^y = x$ can be rewritten in logarithmic form as $\ln(x) = y$, where $\ln$ denotes the natural logarithm (logarithm with base $e$).$\newline$Therefore, the logarithmic form of $e^4 \approx 54.598$ is $\ln(54.598) \approx 4$.

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