Question

what is the solution to the equation below?
\\(\log 7 + \log (x - 4) = 1\\)
\\(\circ\\) \\(x = -\dfrac{38}{7}\\)
\\(\circ\\) \\(x = -\dfrac{18}{7}\\)
\\(\circ\\) \\(x = \dfrac{18}{7}\\)
\\(\circ\\) \\(x = \dfrac{38}{7}\\)

Explanation:

Step1: Apply log product rule

Using the property \(\log a + \log b=\log(ab)\), we get \(\log(7(x - 4)) = 1\).

Step2: Convert log to exponential form

Assuming base 10 (since no base is specified), \(10^1=7(x - 4)\), so \(10 = 7x-28\).

Step3: Solve for x

Add 28 to both sides: \(7x=10 + 28=38\). Then divide by 7: \(x=\frac{38}{7}\).

Answer:

\(x=\frac{38}{7}\) (the option corresponding to \(x = \frac{38}{7}\))