Q:

Logarithmic equation $\log n\le10^6$

I'm trying to solve logarithmic equation (instance below).
$\log{n}\le10^6$
Solution is:
$\log{n}\le10^6\rightarrow2^{\log{n}}\le2^{10^6}\rightarrow n\le2^{10^6}$.
I have no idea how author get this solution. This mean there have a property like $x^{\log{n}}=n$? And how solve this with using real log properties?
Source Row 1 https://udel.edu/~caviness/Class/CISC320-02S/exercise-solns/ch01/R-1.7.pdf

A:

$$\log(n) \le 10^6$$
From the elementary property of the exponential-logarithm we have that
$$\large b^{\log_b(x)} = x ~~~~~~~~~~~ \text{for} ~~~ x > 0;\ ~~ b > 0,\ ~~ b\neq 1$$
From what I understand, your "book" or whatever, uses the ugly notation $\log$ to indicate $\log_2$, the binary logarithm, that is, base $2$. 
Besides the ugliness, we exponentiate in base $2$ then:
$$\large 2^{\log_2(n)} \leq 2^{10^6}$$
$$n \leq 2^{10^6}$$
Which provides the result you were searching for.

