How do you expand #ln ((5sqrty)/x^2)#?

1 Answer
Apr 10, 2018

Answer:

#color(blue)(1/2ln5+1/2lny-2lnx)#

Explanation:

The law of logarithms state:

#log_c(a/b)=log_ca-log_cb#

#log_c(ab)=log_ca+log_cb#

#log_ca^b=blog_ca#

Notice we can write:

#5sqrt(y)=5y^(1/2)#

#:.#

#ln((5sqrt(y))/x^2)=ln((5(y)^(1/2))/x^2)#

# \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \=ln5(y)^(1/2)-lnx^2#

# \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \=1/2ln5y-2lnx#

# \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \=color(blue)(1/2ln5+1/2lny-2lnx)#