# Solve Exponential Equations Using Log Worksheet

## 6 problems

To solve exponential equations using logs, take the logarithm of both sides to bring the exponents down. This transforms the equation into a linear form that can be easily solved for the variable. Solving exponential equations using a log worksheet provides practice problems, and solving exponential equations using logarithms pdf offers a comprehensive guide and examples for mastering this method.

Algebra 2
Exponential Functions

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

• Using logs makes exponential equations simpler and easier to clear up.
• Working with logs helps students understand how logarithms function.
• This technique improves algebra talents through practicing exponent and log regulations.
• Solving these equations boosts logical questioning and careful analysis.
• Students learn to break down complex problems into simpler steps.
• Successfully solving these equations builds confidence with difficult math standards.

## How to Solve Exponential Equations Using Log?

• Start with an equation in the form $$a^x = b$$, where $$a$$ and $$b$$ are constants.
• Take the logarithm of both sides of the equation using a common logarithm (log base 10) or natural logarithm (log base e): $$\log(a^x) = \log(b)$$.
• Utilize the property $$\log(a^x) = x \cdot \log(a)$$ to move the exponent in front: $$x \cdot \log(a) = \log(b)$$.
• Isolate the variable $$x$$ by dividing both sides by $$\log(a)$$: x = \frac{\log(b)}{\log(a)}.

## Solved Example

Q. Solve. Round your answer to the nearest thousandth.$\newline$$7^x = 2$$\newline$$x =$__
Solution:
1. Write Equation: Write down the equation.$\newline$We are given the equation $7^x = 2$. We need to solve for $x$.
2. Apply Logarithm: Apply the logarithm to both sides of the equation.$\newline$To solve for $x$, we can use logarithms. Applying the natural logarithm ($\ln$) to both sides gives us $\ln(7^x) = \ln(2)$.
3. Use Power Property: Use the power property of logarithms. The power property of logarithms states that $\ln(a^b) = b\cdot\ln(a)$. We apply this property to simplify the left side of the equation: $x\cdot\ln(7) = \ln(2)$.
4. Isolate x: Isolate $x$.$\newline$To solve for $x$, we divide both sides of the equation by $\ln(7)$: $x = \frac{\ln(2)}{\ln(7)}$.
5. Calculate Value: Calculate the value of $x$. Using a calculator, we find the values of $\ln(2)$ and $\ln(7)$ and then divide them to find $x$. $x = \frac{\ln(2)}{\ln(7)} \approx \frac{0.69314718}{1.94591015} \approx 0.356207187$
6. Round Answer: Round the answer to the nearest thousandth.$\newline$Rounding the value of $x$ to the nearest thousandth gives us $x \approx 0.356$.

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