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Logarithm to base 2 of $2^n$
I’m having a hard time solving this thing.
I know I should take the logarithm of the base 2 of $2^n$, and then the value of n I want to find should be its exponent. For example, I know the base is 2 and so the logarithm is log_2(x) but then, I don’t know how to take logarithm of $2^n$.
Should I do something like this?
A:
$$\log_2(2^n) = \log_2(2)^n = n \log_2(2)$$
Not sure why you used the expression $2^n$, but I do agree that it is sometimes easier to calculate $\log_b(x)$ than to calculate the base of the power $x^n$.
A:
You can use the following definition of logarithm.
$$\log_b(x) \equiv \frac{\log x}{\log b}$$
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