Question

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

Answer 1

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`