Which Log Operation Applies

Question

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.

score 0 · Accepted Answer · 2018-03-08T16:19:08.200

0

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.

edited Mar 08 '18 at 16:19

answered Mar 08 '18 at 16:15

thank you! so thats the first step down so far – hope1234 Mar 08 '18 at 16:18
@hope1234 But the third step doesn't seem to be correct.! – Mar 08 '18 at 16:19
hmm ok, It was on an answer sheet, I will query it with my professor. – hope1234 Mar 08 '18 at 16:26

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