/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 6 Determine whether each \(x\) -va... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 6

Determine whether each \(x\) -value is a solution (or an approximate solution) of the equation. \(\ln (2 x+3)=5.8\) (a) \(x=\frac{1}{2}(-3+\ln 5.8)\) (b) \(x=\frac{1}{2}\left(-3+e^{5.8}\right)\) (c) \(x \approx 163.650\)

Short Answer

Expert verified
After performing checks on proposed solutions (a), (b) and (c), it is observed that only solution (c) \(x \approx 163.650\) makes the equality hold, hence it is a valid solution to the given equation.

Step by step solution

01

Checking proposed solution (a)

Substitute \(x\) from solution (a) back into the equation, i.e., put \(x=\frac{1}{2}(-3+\ln 5.8)\) into \(\ln (2x+3)=5.8\). Simplifying the left-hand side, will check whether it equals 5.8 or not.
02

Checking proposed solution (b)

Substitute \(x\) from solution (b) back into the equation, i.e., put \(x=\frac{1}{2}\left(-3+e^{5.8}\right)\) into \(\ln (2x+3)=5.8\). Simplifying the left-hand side, will check whether it equals 5.8 or not.
03

Checking proposed solution (c)

Substitute \(x\) from solution (c) back into the equation, i.e., put \(x \approx 163.650\) into \(\ln (2x+3)=5.8\). Simplifying the left-hand side, will check whether it equals 5.8 or not.

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