# Relationship between exponent and logarithm

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

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

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