
Re: Help with logarithms
Posted:
Sep 18, 2006 5:58 PM


> Can somebody help me solve this problems? > > 1) lnx + lnx^2 + lnx^3 + lnx^4 + lnx^5 = 5 > > The answer is sqrt[3](e) > > 2) lnx  ln(2x+1) = ln1/x > > The answer is x=1 + sqrt(2)
1)The equation simplifies to ln(x.x^2.x^3.x^4.x^5) = 5, ln(x^(1+2+3+4+5)) = 5, ln(x^15) = 5, 15 ln(x) = 5, ln(x) = 1/3, x = e^(1/3) = cuberoot of e. 2)ln(x /(2x+1)) = ln(1/x), x /(2x+1) = 1 / x, x^2 = 2x + 1, x^2  2x = 1, x^2  2x + 1 = 2, (x  1)^2 = 2, x  1 = + sqrt(2),(the other value of x  1 is  sqrt(2)which makes x negative) So x = 1 + sqrt(2)

