Math Problem Statement

What is the solution to the expression: ((ln(8.126 / 14.7)) / -0.21) * 5280?

Solution

The mathematical expression in the image can be written as:

(ln(8.12614.7)0.21)×5280\left( \frac{\ln \left( \frac{8.126}{14.7} \right)}{-0.21} \right) \times 5280

Let's solve this step by step:

Step 1: Simplify the fraction inside the natural logarithm

8.12614.7\frac{8.126}{14.7}

Step 2: Take the natural logarithm (ln) of the result from Step 1.

Step 3: Divide by -0.21.

Step 4: Multiply the result by 5280.

I will now compute the solution.The result of the given expression is approximately 14,904.15.

Would you like any further details or explanations about this calculation?

Here are some related questions that might expand on this:

  1. What is the importance of natural logarithms in real-world problems?
  2. How does dividing by a negative number affect the outcome of an equation?
  3. Why is the constant 5280 used in the expression?
  4. Can you provide examples where logarithms are applied in science or engineering?
  5. How can this formula be applied to altitude or pressure calculations?

Tip: Always simplify the expression inside the logarithm before applying the logarithmic function for easier calculations.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Natural Logarithm (ln)
Division by a negative number

Formulas

Natural logarithm: ln(x)
Multiplication and Division
Simplification of fractions

Theorems

Properties of logarithms
Basic arithmetic operations

Suitable Grade Level

Grades 10-12