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In[1]:= Reduce[Log[5, x + 3] == Log[6, x + 14], x]
During the evaluation of In[1]:= Reduce::nsmet: This system cannot be solved with the methods available to Reduce.
Out[1]= Reduce[Log[3 + x]/Log[5] == Log[14 + x]/Log[6], x]
In[2]:= Minimize[(Log[5, x + 3] - Log[6, x + 14])^2, x]
Out[2]= {0, {x -> 22}}