How do you find the domain of f(x)=ln(x2-2x-8)-ln(x2-8x) ?
G ghi New member Joined Dec 26, 2011 Messages 9 Dec 26, 2011 #1 How do you find the domain of f(x)=ln(x2-2x-8)-ln(x2-8x) ?
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,216 Dec 27, 2011 #2 Use the log law \(\displaystyle ln(a)-ln(b)=ln(a/b)\) to write your log as: \(\displaystyle ln(x^{2}-2x-8)-ln(x^{2}-8x)=ln\left(\frac{x^{2}-2x-8}{x^{2}-8x}\right)=ln\left(\frac{(x-4)(x+2)}{x(x-8)}\right)\) \(\displaystyle ln(u)\) is defined when \(\displaystyle u > 0\).
Use the log law \(\displaystyle ln(a)-ln(b)=ln(a/b)\) to write your log as: \(\displaystyle ln(x^{2}-2x-8)-ln(x^{2}-8x)=ln\left(\frac{x^{2}-2x-8}{x^{2}-8x}\right)=ln\left(\frac{(x-4)(x+2)}{x(x-8)}\right)\) \(\displaystyle ln(u)\) is defined when \(\displaystyle u > 0\).