L exp -0.9 S exp 0.40 =1/1000 make L the subject. step by step

To make \( L \) the subject of the equation \( L \cdot e^{-0.9} \cdot S \cdot e^{0.40} = \frac{1}{1000} \), we'll follow these steps:

### Step 1: Simplify the Exponential Terms
Combine the exponential terms using the property \( a \cdot e^{b} \cdot c \cdot e^{d} = (a \cdot c) \cdot e^{b+d} \):

\[
L \cdot S \cdot e^{-0.9 + 0.40} = \frac{1}{1000}
\]

### Step 2: Simplify the Exponent
Simplify the exponent in the exponential term:

\[
L \cdot S \cdot e^{-0.5} = \frac{1}{1000}
\]

### Step 3: Isolate \( L \)
To isolate \( L \), divide both sides of the equation by \( S \cdot e^{-0.5} \):

\[
L = \frac{1}{1000} \div (S \cdot e^{-0.5})
\]

### Step 4: Simplify the Division
Simplify the division by recognizing that dividing by \( e^{-0.5} \) is equivalent to multiplying by \( e^{0.5} \):

\[
L = \frac{1 \cdot e^{0.5}}{1000 \cdot S}
\]

### Step 5: Final Simplified Expression
Thus, the final expression for \( L \) is:

\[
L = \frac{e^{0.5}}{1000 \cdot S}
\]

This is the expression for \( L \) in terms of \( S \).

---

Would you like more details or have any questions? 

Here are 5 related questions to consider:
1. How would you calculate the numerical value of \( e^{0.5} \)?
2. What is the significance of combining exponential terms when simplifying equations?
3. How would you solve for \( S \) if \( L \) and \( e^{0.5} \) are known?
4. Can you express \( L \) in a different form using logarithms?
5. What are some real-world applications of equations involving exponential terms?

**Tip:** When dealing with exponential functions, remember that \( e^{-x} \) can always be rewritten as \( \frac{1}{e^x} \) for easier manipulation.

L exp -0.9 S exp 0.40 = 1/1000 make L the subject. step by step

Follow this detailed, step-by-step solution to make L the subject in the equation L exp -0.9 S exp 0.40 = 1/1000. This problem involves algebraic manipulation of exponential functions, applying key concepts such as the product rule and exponent properties. Ideal 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