Algebraically Show the given equation 2-In(3) + +In(16) 36
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
![**Algebraically Show the Given Equation**
The equation to demonstrate is:
\[ e^{2 \cdot \ln(3) + \frac{1}{2} \ln(16)} = 36 \]
This equation involves using properties of natural logarithms and exponents to simplify and verify the expression.
### Explanation:
1. **Exponent and Logarithm Properties**:
- Use the property \(e^{\ln(x)} = x\).
- The rule for adding logarithms: \(e^{a \cdot \ln(b) + c \cdot \ln(d)} = e^{\ln(b^a \cdot d^c)}\).
2. **Calculation**:
- Simplify \(e^{2 \cdot \ln(3)}\) to \(3^2 = 9\).
- Simplify \(e^{\frac{1}{2} \cdot \ln(16)}\) to \(16^{\frac{1}{2}} = \sqrt{16} = 4\).
3. **Combine Results**:
- This leads to \(9 \cdot 4 = 36\).
Thus, the equation holds true.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc66d6164-0234-4873-be88-e969e82164f6%2F9f910ad9-0577-40bb-81a9-e05e3b055316%2Fe5xa8bd_processed.png&w=3840&q=75)
Transcribed Image Text:**Algebraically Show the Given Equation**
The equation to demonstrate is:
\[ e^{2 \cdot \ln(3) + \frac{1}{2} \ln(16)} = 36 \]
This equation involves using properties of natural logarithms and exponents to simplify and verify the expression.
### Explanation:
1. **Exponent and Logarithm Properties**:
- Use the property \(e^{\ln(x)} = x\).
- The rule for adding logarithms: \(e^{a \cdot \ln(b) + c \cdot \ln(d)} = e^{\ln(b^a \cdot d^c)}\).
2. **Calculation**:
- Simplify \(e^{2 \cdot \ln(3)}\) to \(3^2 = 9\).
- Simplify \(e^{\frac{1}{2} \cdot \ln(16)}\) to \(16^{\frac{1}{2}} = \sqrt{16} = 4\).
3. **Combine Results**:
- This leads to \(9 \cdot 4 = 36\).
Thus, the equation holds true.
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