## anonymous 5 years ago What is the sum of the real solutions to x^(logx) = (x^3)/100 ?

1. anonymous

first take the log of both sides to get the variable out of the exponent. $log(x^{log(x)})=log(\frac{x^3}{100})$ then use the properties of logs so put everything on the ground floor. $log(x)log(x)=log(x^3)-log(100)=3log(x)-2$ hope it is clear than log(100)=2 since 10^2=100 $(log(x))^2=3log(x)-2$ now you have a quadratic equation (in log(x) so set = 0 and solve $(log(x))^2-3log(x)+2=0$ this one factors. $(log(x)-2)(log(x)-1)=0$ two solutions are $log(x)=2$ and $log(x)=1$ now find x $x=10^1$ $x=10^2=100$ total is 110

2. anonymous

Thanks, I remember learning this in the beginning of the year now!