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Disclaimer: I'm new to logs.

I understand the first part of the cancellation property in yellow below. Can anyone explain the second part? I'm confused how you can rewrite it without the a base.

enter image description here

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  • $\begingroup$ hint: $a^? = x$ and $?=\log_a x$ mean the same thing. $\endgroup$ – John Joy Oct 25 '15 at 16:40
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I think I figured this out. It comes from the definition of the inverse of an exponential function:

enter image description here

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  • $\begingroup$ +1 for answering your own question. But it did take you just 13 minutes - you probably could have done it without posting here! $\endgroup$ – Ethan Bolker Oct 25 '15 at 14:10
  • $\begingroup$ Agreed. I'll take it down if nobody finds it useful. $\endgroup$ – mellow-yellow Oct 25 '15 at 14:12
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yes it is right . You can change the position of a and x in second equation so it becomes $x^{log_a^a}$ but $log_a^a$ is 1 so $ x^1 $ =x . Hope this answer helps you understand this property.

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