Question

details
no additional details were added for this assignment.
assignment 6.4: logarithmic equations and inequalities
score: 0/19 answered: 0/16
question 1
solve the equation \\(\ln (6x + 4) = 4\\)
the exact solution (using exponents) is \\(x = \\)
the solution, rounded to 4 decimal places is \\(x = \\)
question help: video message instructor

Explanation:

Step1: Convert log to exponential form

Since $\ln(a)=b$ is equivalent to $e^b=a$, we get:
$$6x + 4 = e^4$$

Step2: Isolate the term with $x$

Subtract 4 from both sides:
$$6x = e^4 - 4$$

Step3: Solve for $x$

Divide both sides by 6:
$$x = \frac{e^4 - 4}{6}$$

Step4: Calculate decimal approximation

First compute $e^4 \approx 54.59815$, then:
$$x \approx \frac{54.59815 - 4}{6} = \frac{50.59815}{6}$$

Answer:

The exact solution (using exponents) is $x = \frac{e^4 - 4}{6}$
The solution, rounded to 4 decimal places is $x = 8.4330$