By definition, we have the following logarithm properties:
[tex]log (A * B) = log (A) + log (B)\\log (A ^ n) = n * log (A)\\log (\sqrt [n] {A}) = \frac {1} {n} * log (A)[/tex]
Now, we can rewrite the given expression as:
[tex]log_ {5} [((5x ^ 3) ^ 2) * \sqrt [3] {x ^ 2 + 6}] =\\log_ {5} (5x ^ 6 * \sqrt [3] {x ^ 2 + 6})[/tex]
Answer:
Option B
