# Solve Multi Step Logarithmic Equations Worksheet

## 6 problems

To solve multi-step logarithmic equations, combine like terms and apply logarithm rules such as product, quotient, and power rules. Isolate the logarithmic term and exponentiate both sides to eliminate the logarithm. Solve the resulting equation for the variable. Verify the solution by substituting it back into the original equation, and check for extraneous solutions. Solving multi-step logarithmic equations step by step offers detailed guidance, ensuring clarity.

Algebra 2
Exponential Functions

## How Will This Worksheet on "Solve Multi-Step Logarithmic Equations" Benefit Your Student's Learning?

• Solving multi-step logarithmic equations helps students grasp complex algebraic concepts.
• Develops problem-solving skills through the application of multiple steps and rules.
• Enhances logical thinking by applying logarithm rules.
• Prepares students for advanced math courses like calculus and algebra.
• Builds confidence in tackling complex mathematical problems.

## How to Solve Multi-Step Logarithmic Equations?

• Start by using logarithm properties to combine multiple logarithmic terms into a single logarithm, if possible. This simplifies the equation.
• Move the combined logarithmic term to one side of the equation and constants to the other side to isolate the logarithm.
• Exponentiate both sides of the equation to eliminate the logarithm and solve for the variable. Remember to apply the correct base for exponentiation.
• Always check your solution by substituting it back into the original equation to ensure it satisfies all conditions and is correct.

## Solved Example

Q. Solve for $r$. $\newline$$2 \, \log_3 (r+1) = 6$ $\newline$Write your answer in simplest form.
Solution:
1. Divide by $2$: First, divide both sides by $2$ to isolate the logarithm.$\newline$$\frac{2 \log_3 (r+1)}{2} = \frac{6}{2}$$\newline$$\log_3 (r+1) = 3$
2. Rewrite in Exponential Form: Rewrite the logarithmic equation in exponential form.$\newline$$3^3 = r+1$$\newline$$27 = r+1$
3. Subtract to Solve for r: Subtract $1$ from both sides to solve for $r$.$\newline$$27 - 1 = r$$\newline$$r = 26$

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