What are the solutions to log sub 6 of open paren x squared plus 8 close paren is equal to 1 plus log sub 6 of x ?

Since the logarithm of x appears, x must be positive. Rewrite 1 as log₆ 6, so the equation becomes log₆(x² + 8) = log₆(6x), which gives x² + 8 = 6x. Factoring gives (x − 2)(x − 4) = 0, so x = 2 or x = 4; both satisfy the domain. The correct choice is A: x is equal to 2 and x is equal to 4.

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