How to square a logarithm?

Question

I am working on some summer work, and I can't seem to remember how to square a log. I need to know what (log(base 3) x)^2 works out to. I'm curious as to what the "laws" of log functions are that would be applied here! Thanks!

Answer 1

log(base n)(x) = log(x)/Log(n)

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

log(a/b) = log(a) - log(b)

log(a^k) = k*log(a)

If y = log(x) then x = e^y

(log(base3)(x))^2 = (log(x))^2/(log(3))^2



(log(x))^2 = log(x^log(x))

Answer 2

Logarithm Squared

Answer 3

There's one simplification that comes to mind here. Log base 3 of x is just asking what you have to raise to 3rd power to get x. That's is if a=log base 3(x) then 3^(a)=x. If you square the log, then your squaring (a): 3^(a^2) = x^a.



One answer suggested that (log(base 3) x)^2 is the same as 2*(log(base 3) x), but this is FALSE. The two is raising the the entire log, not just x.

Answer 4

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Your assumption is wrong. When you take the square root of a number you always potentially have a positive and negative number. Sometimes the problem has a constraint that requires only a positive or only a negative answer.For example - What is the minimum length of fence to enclose a rectangular field that is 1 Hectare in area. A negative length of fence makes no sense so we simply answer 400m. (You could also enclose a 1 hectare field with 4 fences each -100 metres long. Mathematically that is correct but practically it is nonsense.) Common logs are normally used in specific practical problems and practical problems often have constraints. Natural logs are used for theoretical algebraic analysis. In these situations the analysis often uses both roots. Odd roots (3rd, 5th etc.) have one real root. Even roots (4th, 6th etc) have two real roots, one positive and one negative.If you are working with Complex Numbers - that is you allow the use of 'i' the square root of -1 then the nth root of a number has n values. Cube roots of 1 are: 1, -0,5 + 0,8660i, -0.5 - 0.8660i 4th roots of 1 are : 1, i, -1, -i

Answer 5

To multiply using log you simply add them.

But remember a log always equals a log.

You have to take the antilog of the answer to solve it.

The equation you stated is not generally used, as in

algebra you don't multiply logs together if you want

to get a solution in base10. Doing so destroys their

properties, but since you are working in base3 you have

a rather odd excercise going on in number bases.

It appears on the surface that the technique would be used

in something like a random number generator or possibly

cryptology.

Answer 6

Squaring a log doesn't make much sense. I think you mean, for example, finding log x². In that case, it is 2 log x.



For example, log 2² = 2 log 2 = 2 * .30103 = .60206. Look that up in a log table, and you will see it is log 4.

Answer 7

Rule: log base b of m^n is the same thing as n*logbase b of m. The two goes in front.



It's really the same thing as saying (although it doesn't look like it) that if you're raising powers to powers then multiply the exponents together.)

Answer 8

log x^2 = 2logx that's all