Question

Question3 Expand the given expression. Type th 4 In A) 12In(x +1)+ 20 In( 1) -2ln( B) 4 ln

Answer 1

Given expression is = $\ln\left\(\frac{(x+1)^3(x-1)^5}{\sqrt{2x^2-x-1}}\right\)^4$

= $4\ln\left\(\frac{(x+1)^3(x-1)^5}{\sqrt{2x^2-x-1}}\right\)$

= $4[\ln\left\((x+1)^3(x-1)^5\right\)-\ln(\sqrt{2x^2-x-1})]$

= $4[\left\{ \ln\left\((x+1)^3\right\)+\ln((x-1)^5) \right\}-\ln(2x^2-x-1)^{1/2}]$

= $4[3\ln(x+1)+5\ln(x-1)-\frac{1}{2}\ln(2x^2-x-1)]$

= $12\ln(x+1)+20\ln(x-1)-\frac{4}{2}\ln(2x^2-x-1)$

= $12\ln(x+1)+20\ln(x-1)-2\ln(2x^2-x-1)$