Expand to a sum or difference of logarithms: log (subscribt) 5 (25(𝑥−5)^2 /3(x+2)

Question

The 5 is the subscribt, there is one big fraction, please help me with a step by step

Answer 1

log₅(25(x-5)²/(3(x+2)) --> log₅ means log base 5

This expands to:

log₅(25) + log₅((x-5)^2) - log₅(3) - log₅(x+2)

25 = 5² , log_a(a^b) = b, log(b^a) = a log(b)

2 + 2log₅(x+5) - log₅(3) - log₅(x+2)

If you want to simplify more, log₅(3) = ln(3)/ln(5) then add that to 2.