# Solve Exponential Equations Using Ln Worksheet

## 6 problems

To solve exponential equations using $$\ln$$ (natural logarithm), take the natural logarithm of both sides to simplify the exponents. This transforms the equation into a linear form that can be easily solved for the variable. For detailed guidance, solving exponential equations using ln step by step provides a thorough walkthrough, and solving exponential equations using ln calculator offers a quick computational tool.

Algebra 2
Exponential Functions

## How Will This Worksheet on "Solve Exponential Equations Using ln" Benefit Your Student's Learning?

• Using ln simplifies challenging exponential equations.
• Working with ln helps us to understand how logs work better.
• This method improves our algebra skills with logs and exponents.
• Solving equations with ln makes us better at solving tough math problems.
• Learning ln prepares us for more advanced math like calculus.
• Successfully solving these equations builds our confidence with tricky math concepts.

## How to Solve Exponential Equations Using ln?

• Begin with an equation in the form $$a^x = b$$, where $$a$$ and $$b$$ are constants.
• Take the natural logarithm (ln) of both sides: $$\ln(a^x) = \ln(b)$$.
• Utilize the property $$\ln(a^x) = x \cdot \ln(a)$$ to bring the exponent down: $$x \cdot \ln(a) = \ln(b)$$.
• Isolate $$x$$ by dividing both sides by $$\ln(a)$$: x = \frac{\ln(b)}{\ln(a)}.

## Solved Example

Q. Solve for $x$. $\newline$$7=e^x$ $\newline$Round your answer to the nearest thousandth.
Solution:
1. Take Logarithm of Both Sides: $7 = e^x$$\newline$Take the natural logarithm (ln) of both sides.$\newline$$\ln 7 = \ln e^x$
2. Apply Power Property of Logarithms: $\ln 7 = \ln e^x$$\newline$Use the power property of logarithms.$\newline$$\ln 7 = x \ln e$
3. Simplify the Equation: $\ln 7 = x \ln e$$\newline$Since $\ln e = 1$, simplify the equation.$\newline$$\ln 7 = x$
4. Calculate and Round: $\ln 7 = x$$\newline$Calculate $\ln 7$ and round to the nearest thousandth.$\newline$$x \approx 1.945910149$$\newline$$x \approx 1.946$

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