[tex]\ln{[(x^2)(\sqrt{1-x})]}\\ \ln{[(x^2)]}+\ln{[(\sqrt{1-x})]}\\ \ln{[x^2]}+\ln{[\sqrt{1-x}]}\\ 2\ln{[x]}+\ln{[(1-x)^{\frac{1}{2}}]}\\ 2\ln{[x]}+\frac{1}{2}\ln{[1-x]}\\ \\ \ln{[(x)(\sqrt{1+x^2})]}\\ \ln{[(x)]}+\ln{[(\sqrt{1+x^2})]}\\ \ln{[x]}+\ln{[(1+x^2)^{\frac{1}{2}}]}\\ \ln{[x]}+\frac{1}{2}\ln{[1+x^2]}\\ \\ \log_2[\frac{x^3}{x-3}]\\ \log_2[x^3]-\log_2[x-3]\\ 3\log_2[x]-\log_2[x-3]\\ \log[\frac{x(x+2)}{(x+3)^3}]\\ \log[x(x+2)]-\log[(x+3)^3]\\ \log[x]+\log[x+2]-3\log[x+3]\\[/tex]
