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g) 6ln(x) +5 = 17 (x=e² |

g) 6ln(x) +5 = 17 (x=e² |

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Could you explain in detail how to solve these problems? The answers written in red are given to me from the teacher I'm just not sure how they got them. The instructions for these problems say to solve for x

### Transcription for Educational Website #### Problem g: Equation: \( 6 \ln(x) + 5 = 17 \) Solution: - First, isolate the logarithm by subtracting 5 from both sides: \[ 6 \ln(x) = 12 \] - Divide both sides by 6 to solve for \(\ln(x)\): \[ \ln(x) = 2 \] - Exponentiate to solve for \(x\): \[ x = e^2 \] #### Problem h: Equation: \( 2e^{3-x} - 12 = 6 \) Solution: - First, isolate the exponential expression by adding 12 to both sides: \[ 2e^{3-x} = 18 \] - Divide both sides by 2: \[ e^{3-x} = 9 \] - Take the natural logarithm of both sides: \[ 3-x = \ln(9) \] - Solve for \(x\) by isolating it: \[ x = 3 - \ln(9) \] - Simplify further: \[ x = \frac{1}{3} \ln(9) \] These solutions show step-by-step processes to solve logarithmic and exponential equations. The answers are boxed in red for clarity.
Transcribed Image Text:### Transcription for Educational Website #### Problem g: Equation: \( 6 \ln(x) + 5 = 17 \) Solution: - First, isolate the logarithm by subtracting 5 from both sides: \[ 6 \ln(x) = 12 \] - Divide both sides by 6 to solve for \(\ln(x)\): \[ \ln(x) = 2 \] - Exponentiate to solve for \(x\): \[ x = e^2 \] #### Problem h: Equation: \( 2e^{3-x} - 12 = 6 \) Solution: - First, isolate the exponential expression by adding 12 to both sides: \[ 2e^{3-x} = 18 \] - Divide both sides by 2: \[ e^{3-x} = 9 \] - Take the natural logarithm of both sides: \[ 3-x = \ln(9) \] - Solve for \(x\) by isolating it: \[ x = 3 - \ln(9) \] - Simplify further: \[ x = \frac{1}{3} \ln(9) \] These solutions show step-by-step processes to solve logarithmic and exponential equations. The answers are boxed in red for clarity.
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(g) We do only the first part of multiple questions. Please repost the other parts.

Given, 6 ln open parentheses x close parentheses plus 5 equals 17

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