Question

Use the laws of logarithms to expand and simplify the expression.

ln( (x^4)/square root of x(1 + x)^2)

Answer 1

Explanation:

`\ln\left((x^4)/(√(x(1+x)^2))\right)\\=\ln(x^4)-\ln√(x(1+x)^2)\\=4\ln x - \ln √(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))`