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November 8th, 2016, 04:25 AM   #1
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logarithm properties

Hello,
How in this example log changed to exp? with which law?
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November 8th, 2016, 04:34 AM   #2
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$$\log_b x=y \implies b^y=x$$
Or, alternatively and equivalently
$$b^{\log_b x}=x$$
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November 8th, 2016, 04:42 AM   #3
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Thank you but we have exponential.
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November 8th, 2016, 04:47 AM   #4
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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
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Last edited by skipjack; November 8th, 2016 at 04:53 AM.
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November 8th, 2016, 05:02 AM   #5
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As exp is the inverse of log, one can remove log from the left-hand side and put exp in the right-hand side.
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November 8th, 2016, 05:22 AM   #6
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Quote:
Originally Posted by life24 View Post
Thank you but we have exponential.
The $\log$ in the picture means $\log_e$ or $\ln$, the natural logarithm.
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