First you have to use the Change of Base Formula. Hence, log_x(xyz)=ln(xyz)/ln(x), etc.
Then, your equation becomes,
ln(x)/ln(xyz)+ln(y)/ln(xyz)+ln(z)/ln(xyz)=(ln(x)+ln(y)+ln(z))/ln(xyz)=ln(xyz)/ln(xyz)=1
Since, we have the same denominator we can combine everything in a single fraction then using properties of log we get the final answer.
