Change of Base

For a,c>0, a,c 1 and b>0, log_a b= log_c blog_c a Example log_2 5= log_7 5log_7 2 log_112= log_p 2log_p 11, where p>0, p 1. Take note For x,y>0, x,y 1, the reciprocal identity is log_x y= 1log_y x