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

May 31, 2016

ln20

#### Explanation:

Using the following $\textcolor{b l u e}{\text{laws of logarithms}}$

•logx+logy=log(xy).........(1)

•logx-logy=log(x/y).........(2)

•logx^nhArrnlogx...........(3)

using (3) : $2 \ln 5 = \ln {5}^{2} = \ln 25$

using (1) : $\ln 8 + \ln 25 = \ln \left(8 \times 25\right) = \ln 200$

using (2) : $\ln 200 - \ln 10 = \ln \left(\frac{200}{10}\right) = \ln 20$