How do you express #\ln 3+ \frac { 1} { 3} \ln ( 4- x ^ { 2} ) - \ln x# in a single quantity?

1 Answer
Aug 27, 2017

We can simplify to # ln((3root(3)(4 - x^2))/x)#

Explanation:

We will use the following properties of logarithms to answer the problem

#alnn = lnn^a#
#lnn + lnm = ln(n * m)#
#lnn - lnm = ln(n/m)#

Now we can start:

#=ln3 + ln(4 - x^2)^(1/3) - lnx#

#=ln3 + lnroot(3)(4 -x^2) - lnx#

#= ln((3root(3)(4 - x^2))/x)#

Hopefully this helps!