How do you take sqrt(ln(any number))?

Question

How do you take the squareroot of ln of a number, example
sqrt(ln(4))=?

I want to simplify it, without getting a decimal, for instance sqrt(ln(32))=sqrt(5*ln2)

Answer 1

To get an exact answer, just think in opposites and undoing.

How do you undo a square root, in other words, what is the opposite of a square root?

How do you undo a natural logarithm, in other words, what is the opposite of an ln?

Answer 2

Depending on what type of calculator you have, you should work inside out. Find the ln(4), then take the square root of the that result. If you wish to do it by hand, then you could try the change of base formula, but I don't think it would help much. Hope this clears it up for you.

Answer 3

It is the square root of the natural log of 4. Use a calculator.

Answer 4

In ancient days BC, before calculators, we'd look up the log in a table, then look up the square root of that. A few of us knew how to compute a square root longhand, but logs were tables or sliderules or go fish.

Answer 5

Not sure what you mean. There is no property of logarithms which says anything about powers of logs. logs of powers simplify, but not vice verse. If you want the square root of log 4, you get out your calculator.