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How is the property $b^{x+y} = b^x\cdot b^y$ related to the property $\log_b(xy) = \log_b(x)+\log_b(y)$?

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    $\begingroup$ By means of the fact that, when books prove the latter, they write the former, then a "thus", and finally the latter. $\endgroup$ – user228113 May 2 '18 at 7:59
  • $\begingroup$ Welcome to MSE. Please use MathJax. $\endgroup$ – José Carlos Santos May 2 '18 at 8:00
  • $\begingroup$ Review your definition/properties of the logarithm. You should be able to prove the relation between these statements. $\endgroup$ – Yves Daoust May 2 '18 at 8:17
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Very strongly.

Hint: Write $A:=b^x$ and $B:=b^y$.

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