Question

How do you condense $ln 2+2ln3−ln18$?

Answer 1

Hint: In the above problem you were asked to condense ln2+2ln3−ln18. You can solve this problem using the laws of logarithms. There are three laws of logarithms that you can use to solve this problem. So let us see how we can solve this problem.

Complete Step by Step Solution:
In the given question we have to condense ln2+2ln3−ln18. For solving this problem we will use the laws of logarithms. There are three laws of logarithms, they are
 $logx + logy = \log xy$
 $logx-logy = \log (\dfrac{x}{y})$
 $\log {x^n} = n\log x$
On applying these laws of logarithms we get:
 $= \ln 2 + 2\ln 3 - \ln 18$
By applying the second law, we can rewrite $2\ln 3$ as $\ln {3^2}$
 $= \ln 2 + \ln {3^2} - \ln 18$
 $= \ln 2 + \ln 9 - \ln 18$
Putting the values of ln2, ln9 and ln18 we get,
 $= \ln (\dfrac{{2 \times 9}}{{18}})$
By applying the first two laws we get,
 $= \ln (\dfrac{{18}}{{18}})$
 $= \ln 1$
Putting the value of ln1
Value of ln1 is 0, so we get 0.

Therefore, after condensing ln2+2ln3−ln18 we get 0.

Note:
In the above solution, we used the laws of logarithms to solve our problem. It was an easy question of simplification but to solve this you have to learn the laws of logarithms. Also, you need to learn some basic value of logarithm. In this question, we only needed the value of ln1 and laws of logarithms to condense.