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Chapter 3: Problem 94

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$2-6 \ln x=10$$

Short Answer

Expert verified
The solution to the equation is \( x \approx 0.263 \)

Step by step solution

01

Re-arrange the equation

Start off by moving 2 to the right side of the equality. So, the equation becomes: \(-6 \ln x=10 - 2\) or \(-6 \ln x= 8\)
02

Isolate \( \ln x \)

Then, divide both sides by -6 to isolate \( \ln x \). \( \ln x = - \frac{8}{6} \) or \( \ln x = -\frac{4}{3} \)
03

Remove the logarithm

To remove the logarithm, use the property that \( a = b \) implies \( e^a = e^b \), so we find \( x = e^{-\frac{4}{3}} \)
04

Calculate the value of \( x \)

Using the exponential function in the calculator, calculate \( x \) to be approximately 0.263. Check the solution in the original equation to confirm that it is accurate.

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