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If \(log{}_{a}b=c, \) then a=?

Guest Jul 26, 2017
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 #1
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"If  \(log_a b=c\)  then a=?"

 

\(log_ab=c\Rightarrow a^c=b\Rightarrow a=b^{1/c}\)

.

Alan  Jul 26, 2017
edited by Alan  Jul 26, 2017
 #2
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Solve for a:
c = (log(b))/(log(a))

c = (log(b))/(log(a)) is equivalent to (log(b))/(log(a)) = c:
(log(b))/(log(a)) = c

Take the reciprocal of both sides:
(log(a))/(log(b)) = 1/c

Multiply both sides by log(b):
log(a) = (log(b))/c

Cancel logarithms by taking exp of both sides:
Answer: | a = b^(1/c)

Guest Jul 26, 2017

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