I have no idea how to do this!? plz help!?

Question

How do I....

Evaluate

log 1/16
2

the
log
is supposed to have a love exponent of 2
I just dont know how to put it down there beside the "log"

Thanks so much for your help!

Answer 1

I'm assuming you're asking for log 1/16 base 2. Let's call the answer x

Then log 1/16 base 2 = x --> 2^x=1/16

If 2^x=1/16 then 2^-x = 16

2^4=16 so -x=4 so x=-4

Answer 2

Ok, in English you say Log to the Base 2 of 1/16th.

The definition of a Logarithum is: "The power to which the Base is Raised to equal the number in Question".
So, what power do you raise 2 (the base) to so that it equals 1/16?

2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16 , etc. Clearly we aren't getting near 1/16th. But here's the easy part. 2^(-4) = 1/(2^(4)).
So, -4 is the power we raise 2 to in order for it to equal 1/16

So Log base 2 of 1/16 = -4

Answer 3

log base 2 of 1/16 = x(this is the one you wanna know)
then 2^x = 1/16(which is the same as 2^-4)
so x = -4

Answer 4

an exponent of 2 usually means some number is being "squared". To square a number, simply multiply the number times itself. Using standard computer text, the square is usually written (typed?) "^2". The "^" thing is known as a "carat" and is an uppercase "6".

For example, two squared is 2^2 and equals "4". The square of the log of 1/16 would be written "(log(1/16))^2". The double quotes indicate the order of the calculation. I first want to find what the log of the number 1/16 is and having found this number, multiply it by itself.

Answer 5

To write a subscript in text, you use an underscore, like this: log_2 (1/16).

Also, if you wish, you can use the unicode subscript numbers, starting at hex 2080 -- thus you write log₂ (1/16). I recommend downloading this: http://www.cardbox.com/quick.htm . It's saved me a lot of time over the years.

Anyway, you're trying to figure out "what power do I raise 2 to in order to get 1/16?" You know that 2⁴ = 16, so 2⁻⁴ = 1/16, so log₂ (1/16) = -4. (In case the unicode doesn't show up clearly, that's 2^4=16, 2^(-4)=1/16, and log_2 (1/16) = -4, respectively).

Answer 6

log base 2 of (1/16)

The log of a quotient is the difference of the logs. I'll just say log from now on and assume it's base 2, okay:)

log(1/16) = log(1) - log(16)

Now, log(x) means what power do I raise the base to to get x.

I raise 2 to the zero power to get 1 and raise it to the 4 power to get 16, So we have 0 - 4 or -4.

Answer 7

when dealing with a log base 2 the equation can be written as y=log x (log base 2)
rearranging this equation you can come up with the expression x=2^y.
1/16=2^y
therefore y=-4

Answer 8

log base 2 of 1/16 = 2 raised to what power will give you 1/16

log2(n) = ln(n)/ln(2) = log(n)/log(2)

log 1/16/log 2 = -4