Answer:
[tex] 4ln [\frac{x^2 (x^3-1)}{x-5}][/tex]
Step-by-step explanation:
For this case we have the following expression:
[tex] 4[ln(x^3-1) +2ln(x) -ln(x-5)][/tex]
For this case we can apply the following property:
[tex] a log_c (b) = log_c (b^a)[/tex]
And we can rewrite the following expression like this:
[tex] 2 ln(x) = ln(x^2)[/tex]
And we can rewrite like this our expression:
[tex] 4[ln(x^3-1) +ln(x^2) -ln(x-5)][/tex]
Now we can use the following property:
[tex] log_c (a) +log_c (b) = log_c (ab)[/tex]
And we got this:
[tex] 4[ln(x^3-1)(x^2) -ln(x-5)][/tex]
And now we can apply the following property:
[tex] log_c (a) -log_c (b) = log_c (\frac{a}{b})[/tex]
And we got this:
[tex] 4ln [\frac{x^2 (x^3-1)}{x-5}][/tex]
And that would be our final answer on this case.
