Question

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

Answer 1

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`