Solve $LaTeX: \displaystyle \log_{8}(x + 6)+\log_{8}(x + 246) = 4$ .

Using logarithmic properties and expanding the argument gives $LaTeX: \displaystyle \log_{8}(x^{2} + 252 x + 1476)=4$ . Making both sides an exponent on the base gives $LaTeX: \displaystyle x^{2} + 252 x + 1476=8^{4}$ . Expanding and setting equal to zero gives $LaTeX: \displaystyle x^{2} + 252 x - 2620=0$ . Factoring gives $LaTeX: \displaystyle \left(x - 10\right) \left(x + 262\right)=0$ . Solving gives the two possible solutions $LaTeX: \displaystyle x = -262$ and $LaTeX: \displaystyle x = 10$ . The domain of the original is $LaTeX: \displaystyle \left(-6, \infty\right) \bigcap \left(-246, \infty\right)=\left(-6, \infty\right)$ . Checking if each possible solution is in the domain gives: $LaTeX: \displaystyle x = -262$ is not a solution. $LaTeX: \displaystyle x=10$ is a solution.