Logarithms with an answer that is a fraction How does log base 16 of 32 equal 1.25? If we divide 32/16=2 but then if we divide 2/16 it doesn't come out to a whole number unlike with log base 2 of 4 where 4/2=2 and 2/2=1 I am confused why its 1.25 and not simply 1? If we further try to divide with 2/16 we get .125 giving us a total of 1.125 not 1.25. However since 2 can't be divided by 16 it doesn't make sense to keep going. Obviously the answer is 1.25 since 16^(1.25)=32, I'm just not sure how we can get that number.

smekkinnZuG

smekkinnZuG

Answered question

2022-11-23

Logarithms with an answer that is a fraction
How does log base 16 of 32 equal 1.25? If we divide 32 / 16 = 2 but then if we divide 2 / 16 it doesn't come out to a whole number unlike with log base 2 of 4 where 4 / 2 = 2 and 2 / 2 = 1
I am confused why its 1.25 and not simply 1? If we further try to divide with 2 / 16 we get .125 giving us a total of 1.125 not 1.25. However since 2 can't be divided by 16 it doesn't make sense to keep going.
Obviously the answer is 1.25 since 16 1.25 = 32, I'm just not sure how we can get that number.

Answer & Explanation

kjakesHB

kjakesHB

Beginner2022-11-24Added 10 answers

We have that:
log 16 32 = 1.25 = 5 4
Notice that this can also be represented as: 16 5 / 4 = 32
Why? Well, first represent 16 as 2 4
It then follows that: 16 5 / 4 = ( 2 4 ) 5 / 4 = 2 5 = 32
Justine Pennington

Justine Pennington

Beginner2022-11-25Added 2 answers

log 16 32 = 1.25 because 16 1.25 = 32
Recall that in general,
log a b = c means that a c = b
Addendum:
If you are asking how to determine what log 16 32 is, we first change it into exponent form as follows:
log 16 32 = x means 16 x = 32. We then take the log of both sides.
log 16 x = log 32
Then using the property of logs that lets us move the exponent down (i.e, log x n = n log x ), we can simplify this to
x log 16 = log 32 x = log 32 log 16 = 1.25

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