# How do you condense Ln x + 2Ln y?

Jun 1, 2016

$\ln \left(x {y}^{2}\right)$

#### Explanation:

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

•logx+logy=log(xy).............(1)

•logx^nhArrnlogx................(2)

Although expressed in terms of log ,these laws apply to logs of any base.

using (2) : $2 \ln y = \ln {y}^{2}$

using (1) : $\ln x + \ln {y}^{2} = \ln \left(x {y}^{2}\right)$

$\Rightarrow \ln x + 2 \ln y = \ln \left(x {y}^{2}\right)$

Jun 1, 2016

$\ln \left(x {y}^{2}\right)$

#### Explanation:

$\textcolor{b l u e}{\text{Introduction to some principles of logs}}$

Multiplication of source numbers results in addition of logs.

So $\log \left(a b\right) = \log \left(a\right) + \log \left(b\right)$

The product of a constant and a log is the consequence of the source value raised to the power of that constant.

$2 \log \left(a\right) = \log \left({a}^{2}\right)$

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$\textcolor{b l u e}{\text{Answering your question}}$

Consider: $2 \ln \left(y\right)$

Another way of writing this is: $\ln \left({y}^{2}\right)$

Consider: $\ln \left(x\right) + \ln \left({y}^{2}\right)$

Another way of writing this is: $\ln \left(x {y}^{2}\right)$