TITLE: Is this equation valid $\gamma b^{e \log_b{n+e}} = \gamma b^e + n^e$,?
QUESTION [2 upvotes]: While reading a script I found this equation:
$\gamma b^{e \log_b{n+e}} = \gamma b^e + n^e$ 
and i cannot figure out how the author did this. I'd appreciate a step-by step equation for this equation.

REPLY [4 votes]: By the definition of the logarithm 
$b^{\log_b n}=n$, so following the usual rules of powers of power: $b^{e\log_b n}=(b^{\log_b n})^e=n^e$. Another rule about powers is $b^{x+y}=b^x\cdot b^y$, so altogether we get $b^{e\log_b n+e}=b^{e\log_bn}\cdot b^e=n^e\cdot b^e$. 
Therefore it should read
$$\gamma b^{e\log_b n+e}=\gamma b^e\cdot n^e,$$
and it looks like a multiplication sign was accidentally converted to a plus sign.
{"set_name": "stack_exchange", "score": 2, "question_id": 308282}