My Math Forum logarithm properties

 Pre-Calculus Pre-Calculus Math Forum

November 8th, 2016, 03:25 AM   #1
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logarithm properties

Hello,
How in this example log changed to exp? with which law?
Thanks
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 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 $$b^{\log_b x}=x$$ Thanks from life24
 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 timey-wimey 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 Thanks from life24 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 left-hand side and put exp in the right-hand side. Thanks from life24
November 8th, 2016, 04:22 AM   #6
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Math Focus: Mainly analysis and algebra
Quote:
 Originally Posted by life24 Thank you but we have exponential.
The $\log$ in the picture means $\log_e$ or $\ln$, the natural logarithm.

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