explain me in steps how to do log2 (x) - log4 (x+4)
To simplify log2 (x) - log4 (x+4), you can use the property of logarithms that states log_a (x) - log_a (y) = log_a (x/y). Here are the steps to simplify this expression:
1. Use the property of logarithms to rewrite the expression as a single logarithm: log2 (x) - log4 (x+4) = log2(x / (x+4))
2. To simplify further, you can combine the two terms in the numerator by finding a common denominator. In this case, the common denominator is 4, so rewrite the expression as: log2((4x) / (4(x+4)))
3. Now, simplify the expression within the logarithm: log2(4x / (4x + 16))
4. Further simplify by dividing both the numerator and the denominator by 4: log2(x / (x + 4))
Therefore, log2 (x) - log4 (x+4) simplifies to log2(x / (x + 4)).