We know that :
[tex]\clubsuit[/tex] [tex]ln(A) - ln(B) = ln(\frac{A}{B})[/tex]
[tex]\clubsuit[/tex] [tex]aln(x) = ln(x)^a[/tex]
[tex]\clubsuit[/tex] [tex]ln(A) + ln(B) = ln(AB)[/tex]
Using above ideas we can solve the Problem :
⇒ [tex]\frac{3}{8}ln(x + 3) = ln(x + 3)^\frac{3}{8}[/tex]
⇒ [tex]ln(x - 3) - ln(x + 3)^\frac{3}{8} = ln[\frac{(x - 3)}{(x + 3)^\frac{3}{8}}][/tex]
⇒ [tex]4ln[\frac{(x - 3)}{(x + 3)^\frac{3}{8}}] = ln[\frac{(x - 3)}{(x + 3)^\frac{3}{8}}]^4 = ln[\frac{(x - 3)^4}{(x + 3)^\frac{3}{2}}][/tex]
⇒ [tex]\frac{1}{3}lnx + ln[\frac{(x - 3)^4}{(x + 3)^\frac{3}{2}}] = ln(x)^\frac{1}{3} + ln[\frac{(x - 3)^4}{(x + 3)^\frac{3}{2}}] = ln[\frac{\sqrt[3]{x}(x - 3)^4}{\sqrt{(x + 3)^{3}}}][/tex]
Option 3 is the Answer
