How to express a sum of logarithms for log_5(125*25)?

mooltattawsmq8

mooltattawsmq8

Answered question

2023-01-08

How to express a sum of logarithms for log5(12525)?

Answer & Explanation

Armeebildzku

Armeebildzku

Beginner2023-01-09Added 14 answers

logb(x×y)=logbx+logby
log5(125×25)=log5125+log525
Asaoflogarithms:log5(125×25)=log5125+log525
Mara Boyd

Mara Boyd

Beginner2023-01-10Added 2 answers

Prelimaries
Note that loga(x)=log10(x)log10(a)
Actually this still works if a=10 as we have:
log10(x)=log10(x)log10(10)=log10(x)1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Lkgatthequestion
Known: 125×25=3125
So we have: log5(3125)
This results from converting to log base 10:
log10(3125)log10(5)=3.494850.69897
log10(3125)log10(5)=5Solution(1)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~lkgatmizsanswer
They state the answer as log5(125)+log5(25)
log10(125)log10(5)+log10(25)log10(5)
ddd3ddddd+dd2dddd=5Solution(2)

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