[n = \frac{\log(34100 / 34405)}{\log(1 + 0.13)}
]

To solve the given equation for \( n \):

\[
n = \frac{\log\left(\frac{34100}{34405}\right)}{\log(1 + 0.13)}
\]

### Step 1: Simplify the fraction inside the logarithm.
\[
\frac{34100}{34405} \approx 0.99115
\]

### Step 2: Compute the logarithms.
Using base-10 logarithms:

\[
\log(0.99115) \approx -0.00381
\]
\[
\log(1 + 0.13) = \log(1.13) \approx 0.05308
\]

### Step 3: Solve for \( n \).
\[
n = \frac{-0.00381}{0.05308} \approx -0.0717
\]

So, the value of \( n \) is approximately:
\[
n \approx -0.0717
\]

Let me know if you'd like further details on this calculation.

### Relative questions:
1. What are logarithms, and how are they used in solving equations?
2. How does changing the base of a logarithm affect the result?
3. Why did we use the base-10 logarithm in this case?
4. What are some common applications of logarithmic equations in real life?
5. How can you interpret a negative result for \( n \) in this context?

### Tip:
Always check the domain of the logarithmic function to ensure the arguments are positive before applying logarithms.

n = \frac{\log(34100 / 34405)}{\log(1 + 0.13)}

Learn how to solve the logarithmic equation n = log(34100 / 34405) / log(1 + 0.13) with a detailed step-by-step solution. This problem involves logarithms, base-10 computations, and algebraic fraction simplification, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation