+0  
 
0
293
2
avatar

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

Guest Jul 26, 2017
 #1
avatar+26837 
+2

"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
avatar
+2

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

16 Online Users

avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.