Which Log Operation Applies

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Hello I would like to know which log rule applies below:

This step is given:

$$2n \left(1 - \left(\dfrac 12\right)^{\log n + 1}\right)$$

This is followed by this step:

$$2n - n\left(\dfrac 12\right)^{\log n}$$

Which is then followed by:

$2n - \dfrac nn$

Could I get an explanation for each step please? Sorry for being so much of a novice.

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Apply this exponential property in the first step:

$$a^{b+c}=a^b\cdot a^c$$

Where $a=\dfrac 12$, $b=\log n$, and $c=1$

(Along with distribution of $2n$)

However, I do not know how they got from the second to the third step, the third step seems to be wrong.