How do you condense #ln 8 + 2ln 5 - ln 10#?

1 Answer
May 31, 2016

Answer:

ln20

Explanation:

Using the following #color(blue)"laws of logarithms"#

#•logx+logy=log(xy).........(1)#

#•logx-logy=log(x/y).........(2)#

#•logx^nhArrnlogx...........(3)#

using (3) : #2ln5=ln5^2=ln25#

using (1) : # ln8+ln25=ln(8xx25)=ln200#

using (2) : #ln200-ln10=ln(200/10)=ln20#