Help with radical logs. log_ 2 sqrt(32)

Anton Huynh

Anton Huynh

Answered question

2022-11-05

Help with radical logs. log 2 32
I am having trouble understanding logarithms. Specifically I can't understand this equation.
log 2 32
I know the answer is ( 5 2 ) but I don't know how it is the answer. If somebody could please explain the process step by step for solving this log and perhaps give examples of other radical logs I would really appreciate it.

Answer & Explanation

lelestalis80d

lelestalis80d

Beginner2022-11-06Added 23 answers

Using Logarithmic formula
log e ( m ) n = n log e ( m ) ,
where m > 0 and
log m ( m ) = 1 ,
Where m > 0 and m 1
So
log 2 32 = log 2 ( 32 ) 1 2 = log 2 ( 2 5 ) 1 2 = log 2 ( 2 ) 5 2 = 5 2 log 2 ( 2 ) = 5 2
Alexia Avila

Alexia Avila

Beginner2022-11-07Added 4 answers

Hint :
32 = 32 1 2 = 2 5 2

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