the expression (log2)16/(log2)(1/2) is?

Question

A)-4
B)3
C)5
D)32

Answer 1

log(2)16 = 4
log(2)(1/2) = -1
=>
(log2)16/(log2(1/2)) = -4

Answer 2

Looks complicated but isn't. Usually best to re-write expression in an order which looks simpler to you: example,

16 (log2) / (1/2) (log2) =
16 (log2) / (0.5) (log2) =
16 / (0.5) = 32

So the answer is D) 32.

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If the notation (log2)16 means log of 16 to the basis of 2, then the previous 2 answers yielding -4 is correct. Working in reverse from those answers by factoring :

16 = 2^4 so (log2)16=4;
1/2 = 2(^-1) so (log2)(1/2)=-1

therefore
(log2)16/(log2)(1/2) = 4/(-1) = -4.




Don't clutch up at all those mixed up expressions. Re-write the expressions in a simpler way for you to read.

Answer 3

(log2)(16)/(log2)(1/2)

This is ambiguous. Do you mean:

(log2)(16)/{(log2)(1/2)}

or

{(log2)(16)/(log2)}(1/2)

Either way, start by dividing numerator and denominator by log2.

I'll take the first one.

(log2)(16)/{(log2)(1/2)}
= 16/(1/2) = 32

The answer is D).

I should add one more. Does log2 mean
The (log of 2) or (log to the base 2)?

If it means log to the base 2 then the answer is:

(log2)16/(log2)(1/2)
4/-1 = -4
The answer is A).

Please state your questions clearly in the future. We shouldn't have to guess at what the question is supposed to be.

Answer 4

Helmut, Patrick M and Chetan all have the correct answer. However, some of these people here seem to be reading your problem incorrectly.

log (base 2) 16 = 4, because (2)^4 = 16.

log (base 2) 1/2 = -1, because (2)^-1 = 2^(0-1) = 2^0/2^1 = 1/2.

Therefore, log (base 2) 16 / log (base 2) 1/2 = 4 / -1 = -4.

Answer 5

(log2)16/(log2)(1/2) =
4/-1 =
-4

Answer 6

answer is D. 32

Answer 7

Correct answer is -4.

Answer 8

a) listen in class
b) get tutoring
c) use a calculator
d) all of the above

the answer is d