Consider the following exponential equation. e5x + 2 = 900 Rewrite the equation by taking the natural logarithm of both sides. Simplify completely using properties of logarithms. (5.x+2) · In(e) × = In(900) Solve the exponential equation for the unknown x. (Round your answer to four decimal places.) X =
Consider the following exponential equation. e5x + 2 = 900 Rewrite the equation by taking the natural logarithm of both sides. Simplify completely using properties of logarithms. (5.x+2) · In(e) × = In(900) Solve the exponential equation for the unknown x. (Round your answer to four decimal places.) X =
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Consider the following exponential equation.
\[ e^{5x + 2} = 900 \]
Rewrite the equation by taking the natural logarithm of both sides. Simplify completely using properties of logarithms.
\[ (5 \cdot x + 2) \cdot \ln(e) = \ln(900) \]
Solve the exponential equation for the unknown \( x \). (Round your answer to four decimal places.)
\[ x = \Box \]
**Explanation of the image content:**
- The original equation is an exponential equation where \( e \) raised to the power of \( 5x + 2 \) equals 900.
- The next step involves taking the natural logarithm of both sides to simplify the equation. Since \(\ln(e) = 1\), the equation reduces to \( 5x + 2 = \ln(900) \).
- The task is to solve for \( x \) and round the answer to four decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc20ba261-3077-4da5-9466-d35d0dacb76b%2Fa648f136-3fe8-4d8b-8653-4ccc6db49006%2Fze00te_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following exponential equation.
\[ e^{5x + 2} = 900 \]
Rewrite the equation by taking the natural logarithm of both sides. Simplify completely using properties of logarithms.
\[ (5 \cdot x + 2) \cdot \ln(e) = \ln(900) \]
Solve the exponential equation for the unknown \( x \). (Round your answer to four decimal places.)
\[ x = \Box \]
**Explanation of the image content:**
- The original equation is an exponential equation where \( e \) raised to the power of \( 5x + 2 \) equals 900.
- The next step involves taking the natural logarithm of both sides to simplify the equation. Since \(\ln(e) = 1\), the equation reduces to \( 5x + 2 = \ln(900) \).
- The task is to solve for \( x \) and round the answer to four decimal places.
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