Question

Condense.

14.) 3lnx+2lny-4lnz

16.) 3/2 (ln(x^2+1)-ln(x+1)-ln(x-1))

#15 is in photo

Answer 1

See below for answers and explanations

Explanation:

Problem 14

`\displaystyle 3\ln(x)+2\ln(y)-4\ln(z)\\\\=\ln(x^3)+\ln(y^2)-\ln(z^4)\\\\=\ln(x^3y^2)-\ln(z^4)\\\\=\ln\biggr((x^3y^2)/(z^4)\biggr)`

Problem 15

`\displaystyle2\log_2(3)-(1)/(2)\log_2(x^2+1)\\\\=\log_2(3^2)-\log_2(√(x^2+1))\\\\=\log_2\biggr((9)/(√(x^2+1))\biggr)`

Problem 16

`\displaystyle (3)/(2)\biggr(\ln(x^2+1)-\ln(x+1)-\ln(x-1)\biggr)\\\\= (3)/(2)\biggr(\ln\biggr((x^2+1)/(x+1)\biggr) -\ln(x-1)\biggr)\\\\= (3)/(2)\ln\biggr((x^2+1)/((x+1)(x-1))\biggr)\\\\=\ln\biggr(\biggr((x^2+1)/(x^2-1)\biggr)^{(3)/(2)}\biggr)`