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I know how to solve if the left side is just lgn, but it has an extra n. Was it correct to multiply both sides by e?

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    I have honestly never seen "lgn" before. What does it mean? – 2017-01-30
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    @TheCount Usually, $\operatorname{lg}=\log_2$. – 2017-01-30
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    @SimplyBeautifulArt OK, that's what I assumed from the context. Is it more common outside the US? Or is it somewhat esoteric? – 2017-01-30
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    OK, I don't understand your last step. Care to explain it? – 2017-01-30
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    There is no solution in elementary functions for a problem such as this. You might want to look at the [Lambert W-function](https://en.wikipedia.org/wiki/Lambert_W_function) – 2017-01-30

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That is not the correct way to do it. Indeed, checking your answer into the original line, it is obvious this is false. Instead, note the Lambert W function:

$$n\ln(n)=\ln(n)e^{\ln(n)}=10^6\ln(2)$$

$$\implies\ln(n)=W_0(10^6\ln(2))$$

$$\large n=e^{W_0(10^6\ln(2))}$$