If log2 5 = a, log2 3 = b and log2 7 = c, determine an expression for log2 (25/21) in terms of a, b, and c

Step-by-step explanation: We know that:

and we want:

.

We can form the numerator using just the first fact (since 5^2 is 25) and the denominator using the latter two (since 3*7 = 21).

The logarithm of a division can be expanded by subtracting the numerator and denominator (while still keeping the log). The logarithm of a product can be expanded by adding the terms while keeping the log. If the logarithm is raised to a power, we can bring it down as a factor:

.

Substituting the variables:

2

step-by-step explanation: