How do you simplify #2 log_10 sqrt(x) + 3 log_10 x^(1/3)#?

1 Answer
Apr 12, 2016

Answer:

found: #2log_(10)x#

Explanation:

We can use the fact that:
1) #sqrt(x)=x^(1/2)#
and
2) #logx^m=mlogx#
to write:
#2log_(10)sqrt(x)+3log_(10)x^(1/3)=#
#=2log_(10)x^(1/2)+3*1/3log_(10)x=#
#=cancel(2)*1/cancel(2)log_(10)x+cancel(3)*1/cancel(3)log_(10)x=2log_(10)x#