The solutions for \(\log x + \log (3\cdot x - 13) = 1\) are \(x_{1} = 5\) and \(x_{2} = -\frac{2}{3}\), respectively.
In this question, we are going to solve for \(x\) with the help of Logarithm Properties, which are described in the image attached below.
\(\log x + \log (3\cdot x - 13) = 1\)
\(\log [x\cdot (3\cdot x - 13)] = 1\)
\(\log (3\cdot x^{2}-13\cdot x) = 1\)
\(10^{\log(3\cdot x^{2}-13\cdot x)} = 10^{1}\)
\(3\cdot x^{2}-13\cdot x = 10\)
\(3\cdot x^{2}-13\cdot x -10 = 0\)
This is a Second Order Polynomial, which can be solved by Quadratic Formula:
\(x_{1} = 5\) and \(x_{2} = -\frac{2}{3}\)
The solutions for \(\log x + \log (3\cdot x - 13) = 1\) are \(x_{1} = 5\) and \(x_{2} = -\frac{2}{3}\), respectively.
Please see this question related to Logarithm Properties for further details:
https://brainly.com/question/12983107
