Value of the logarithmic expression Why log_6 sqrt(6)=1/2? I know that sqrt(6) = 6^(1/2)

Kasey Reese

Kasey Reese

Answered question

2022-10-21

Value of the logarithmic expression
Why log 6 6 = 1 / 2?
I know that 6 = 6 1 / 2

Answer & Explanation

Momellaxi

Momellaxi

Beginner2022-10-22Added 14 answers

Since 6 = 6 1 / 2 we have:
log 6 6 = log 6 6 1 / 2 = 1 / 2
You can think of log 6 n as "the exponent I need to apply to 6 in order to obtain n". Well, since in this particular case n = 6 1 / 2 it follows naturally that the exponent you need to apply is in fact 1 / 2
You can also evaluate the expression using these properties of logarithms:
log a b c = c log a b log a a = 1
You can check that: log 6 6 1 / 2 = 1 2 log 6 6 = 1 2
Rubi Garner

Rubi Garner

Beginner2022-10-23Added 4 answers

So what is a logarithm?
It is essentially the exponent value required, with a particular base, to give the value. In the equation below it is easy to see that x must 2. 6 is the base and x is the exponent.
6 x = 36
The logarithm is the formal definition of this relationship.
L o g 6 ( 6 1 2 ) = x
Let's rewrite that in the same style as the first:
6 x = 6 1 2
So obviously x must be 1 2 . But if you notice the 6 is common to both sides and you really only care about the exponents, and that's where the log comes in.

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