Question

what are the potential solutions of \\(\log_{6}x + \log_{6}(x + 5) = 2\\)?
-12
-9
4
32
36

what is the solution of \\(\log_{6}x + \log_{6}(x + 5) = 2\\)?

Explanation:

Apply the product rule for logarithms

Using the Logarithmic Product Rule knowledge point

$$
LATEXBLOCK0
$$

Convert to exponential form

Using the Solving Logarithmic Equations knowledge point

$$
LATEXBLOCK1
$$

Solve the quadratic equation

Using the Polynomial Factoring knowledge point

$$
LATEXBLOCK2
$$

These are the potential solutions.

Check for extraneous solutions

Using the Extraneous Solutions knowledge point

$$
LATEXBLOCK3
$$

Answer:

Question 1

The potential solutions of \(\log_{6}x + \log_{6}(x + 5) = 2\) are:

• \(-9\)
• \(4\)

Question 2

The actual solution of \(\log_{6}x + \log_{6}(x + 5) = 2\) is:

• \(4\)