Question

What is 2 log subscript 5 baseline (5 x cubed) + one-third log subscript 5 baseline (x squared + 6) written as a single logarithm? log subscript 5 baseline (25 x superscript 5 baseline) rootindex 3 startroot x squared + 6 endrot log subscript 5 baseline (25 x superscript 6 baseline) rootindex 3 startroot x squared + 6 endroot log subscript 5 baseline 25 x superscript 5 baseline + log subscript 5 baseline 2 + log one-third x squared (log subscript 5 baseline 25 + log subscript 5 baseline superscript 6 baseline) (log subscript 5 baseline rootindex 3 startroot x squared + 6 endroot).

Answer 1

Using the properties $n\log_a(b) = \log_a(b^n)$ and $\log_a(b) + \log_a(c) = \log_a(bc)$, we have

2 log₅ (5x³) + 1/3 log₅ (x² + 6)

= log₅ (5x³)² + log₅ ∛(x² + 6)

= log₅ (25x⁶) + log₅ ∛(x² + 6)

= log₅ (25x⁶ ∛(x² + 6))

Trying to parse the choices you listed is ... difficult. I trust you'll be able to figure out which one matches best on your end.

Answer 2

Answer:

B

Explanation:

On edge