Logarithm expression

Question

3logx+ 2log7- log y

 

1/2lnx-2/3lnx

Answer 1

Let's SIMPLIFY 3logx+ 2log7- log y

= LOG [x³•7² ÷ y] = log(49x³/y]

 

Let's simplify 1/2lnx-2/3lnx

First, factor:  (ln x)(1/2 - 2/3) = (-1/6)(ln x) = ln x^-1/6  = ln (1/x^1/6) = ln1 - ln ('sixth root of x') = - ln 'sixth root of x' 

since ln 1 = 0

Note: either of the two boldface answers above is good.