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November 8th, 2016, 03:25 AM  #1 
Senior Member Joined: Feb 2014 Posts: 112 Thanks: 1  logarithm properties
Hello, How in this example log changed to exp? with which law? Thanks 
November 8th, 2016, 03:34 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,305 Thanks: 2443 Math Focus: Mainly analysis and algebra 
$$\log_b x=y \implies b^y=x$$ Or, alternatively and equivalently $$b^{\log_b x}=x$$ 
November 8th, 2016, 03:42 AM  #3 
Senior Member Joined: Feb 2014 Posts: 112 Thanks: 1 
Thank you but we have exponential.

November 8th, 2016, 03:47 AM  #4 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,797 Thanks: 715 Math Focus: Wibbly wobbly timeywimey stuff. 
What v8archie is trying to say is, just take the exponential of both sides. $\displaystyle \log(x) = y \implies x = e^y$ (This is assuming that log means "log with the base e.") Dan Last edited by skipjack; November 8th, 2016 at 03:53 AM. 
November 8th, 2016, 04:02 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,951 Thanks: 1599 
As exp is the inverse of log, one can remove log from the lefthand side and put exp in the righthand side.

November 8th, 2016, 04:22 AM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,305 Thanks: 2443 Math Focus: Mainly analysis and algebra  

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