What is 2log(2) expressed in log(c)?

To express 2log(2) in terms of log(c), we need to use the properties of logarithms. The question doesn't specify the base of the logarithm, but since we're dealing with "log" and not "ln," I'll assume the base is 10. So, log(2) means log base 10 of 2.

The expression 2log(2) can be rewritten using the power rule of logarithms, which states that:

n * log base b (a) = log base b (a^n)

So, in the case of 2log(2):

2log(2) = log(2^2) = log(4)

Now, to express log(4) in terms of log(c), where c is any number, we use the change of base formula. This formula allows us to change the base of a logarithm using the following equation:

log base b (a) = log base c (a) / log base c (b)

Applied to log(4) in terms of log(c), we get:

log(4) = log(c) (4) / log(c) (10)

So, 2log(2) can be expressed in terms of log(c) as:

2log(2) = log(c) (4) / log(c) (10)