Question29. Solve the equation. $$\log _{6}(x)=\log _{6}\left(\frac{1}{x}\right)+8$$

Studdy Solution
Solve for $x$ by taking the square root of both sides. Remember to consider both the positive and negative roots:
$x = \pm \sqrt{6^8}$
$x = \pm 6^4$
$x = \pm 1296$
The solutions for $x$ are:
$$x = 1296 \quad \text{and} \quad x = -1296$$
However, since $x$ must be positive in the context of logarithms, the valid solution is:
$$\boxed{1296}$$