Question

Use the laws of logarithms to expand and simplify the expression.
ln( (x^4)/square root of x(1 + x)^2)

Answer 1

Answer:

Step-by-step explanation:

$\ln\left(\frac{x^4}{\sqrt{x(1+x)^2}}\right)\\=\ln(x^4)-\ln\sqrt{x(1+x)^2}\\=4\ln x - \ln \sqrt{x} - \ln (1+x)\\=4\ln x-(1/2)\ln x -\ln(1+x)\\=(9/2)\ln x - \ln(1+x)\\=\ln x^{9/2}-\ln(1+x}\\=\ln (x^{9/2}/(1+x))$