Solve $LaTeX: \displaystyle \log_{8}(x + 247)+\log_{8}(x + 7) = 4$ .

Using logarithmic properties and expanding the argument gives $LaTeX: \displaystyle \log_{8}(x^{2} + 254 x + 1729)=4$ . Making both sides an exponent on the base gives $LaTeX: \displaystyle x^{2} + 254 x + 1729=8^{4}$ . Expanding and setting equal to zero gives $LaTeX: \displaystyle x^{2} + 254 x - 2367=0$ . Factoring gives $LaTeX: \displaystyle \left(x - 9\right) \left(x + 263\right)=0$ . Solving gives the two possible solutions $LaTeX: \displaystyle x = -263$ and $LaTeX: \displaystyle x = 9$ . The domain of the original is $LaTeX: \displaystyle \left(-247, \infty\right) \bigcap \left(-7, \infty\right)=\left(-7, \infty\right)$ . Checking if each possible solution is in the domain gives: $LaTeX: \displaystyle x = -263$ is not a solution. $LaTeX: \displaystyle x=9$ is a solution.