Find the exact value of log5 0.2
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calendarEducator since 2008
write3,662 answers
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We need to determine the exact value of the logarithm expression log5 0.2
First we will rewrite 0.2 = 2/10
==> log5 0.2 = log5 (2/10) = log 5 (1/5)
Now we will use the logarithm properties to simplify.
We know that log a/b = log a - log b
==> log5 (1/5) = log5 1 - log 5 5
Now we know that loga 1 = 0 and loga a = 1
==> log5 (1/5) = 0 - 1 = -1
Then the exact value of log5 0.2 = -1
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calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
We have to find the value of log(5) 0.2.
0.2 = 1/5 = 5^-1
Now log a^b = b*log a. And log(a) a = 1
log(5) 0.2
=> log (5) [ 1/5]
=> log (5) [ 5^-1]
=> -1* log(5) 5
=> -1*1
=> -1
Therefore the required value of log(5) 0.2 = -1.