2logx+3logx=10

2logx+3logx=10

$$\\logx^2+logx^3=10\\\\ log(x^2*x^3)=10\\\\ log(x^5)=10\\\\ 10^{log(x^5)}=10^{10}\\\\ x^5=10^{10}\\\\ (x^5)^{1/5}=(10^{10})^{1/5}\\\\ x=10^2\\\\ x=100$$

OR BETTER STILL

2logx+3logx=10

$$\\5logx=10\\\\ logx=2\\\\ x=10^2\\\\ x=100$$

BUT why do it the easy way when there is a perfectally good difficult route that can be traversed?   :))