SOLUTION: Hello! I was exploring logarithm and found a quetion with a solution that wasn't very clear to me. So I need your help. The problem was "the logarithm of 20 to the base 5 + the lo

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Question 88306: Hello! I was exploring logarithm and found a quetion with a solution that wasn't very clear to me. So I need your help.
The problem was "the logarithm of 20 to the base 5 + the logarithm of 1/4 to the base 4" so what is the solution to that problem? Can you please explain it to me step by step.
Thank you very much for your support.
Answer by malakumar_kos@yahoo.com(315) (Show Source):
You can put this solution on YOUR website!

"the logarithm of 20 to the base 5 + the logarithm of 1/4 to the base 4"
log of 20 to the base 5 + log of 1/4 to the base 4 can be written as
log 4.5 to base 5+log 1/4 to base 4
= log 4 to base 5+log 5 to the base 5+ log 1 to base 4- log 4 to base 4
[ using the property of logarithms]
= log 4 to base 5 + 1+log 1 to base 4 - 1 [log of any number to the base of the same number is always = 1]
= log 4 to base 5+ log 1 to base 4 [reduce both log to the same base i.e 10]
= log 4 to base 10/log 5 to base 10 + log 1 to base 10/ log 4 to base 10
since all the log's are to the same base use the property of logarithms
= log(4/5)+log(1/4) = log4 - log5+log 1- log4 = -log 5 to the base10