Question

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

Answer 1

`ln(xy^2)`

Explanation:

Using the `color(blue)"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) : `2lny=lny^2`

using (1) : `lnx+lny^2=ln(xy^2)`

`rArrlnx+2lny=ln(xy^2)`

Answer 2

`ln(xy^2)`

Explanation:

`color(blue)("Introduction to some principles of logs")`

Multiplication of source numbers results in addition of logs.

So `log(ab)=log(a)+log(b)`

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

`2log(a) = log(a^2)`

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`color(blue)("Answering your question")`

Consider: `2ln(y)`

Another way of writing this is: `ln(y^2)`

Consider: `ln(x)+ln(y^2)`

Another way of writing this is: `ln(xy^2)`