Question

Enhanced Assignment Express in terms of sums and differences of logarithms. ln(6)/(7x^(7)y)

Answer 1

The expression ln(6)/(7x^7y) can be broken down into sums and differences of logarithms using the properties of logarithms, resulting in the following: ln(6)/7 - 7*ln(x) - ln(y).

Step-by-step explanation:

To express a logarithm in terms of sums and differences, we can use the properties of logarithms. Here, we have: ln(6)/(7x^7y).

We can divide the expression into two parts:

1. ln(6)/7 - which we will leave as it is because 6 is a constant
2. ln(1/(x^7y)) - we use the property of logarithms that says ln(1/a) = -ln(a)

So, the full expression becomes: ln(6)/7 - ln(x^7y). Then, we can break down the second part of the expression further using the property of logarithms that says ln(a*b) = ln(a) + ln(b). So, we end up with: ln(6)/7 - (ln(x^7) + ln(y)). At last using another properties of logs, which is ln(a^b) = b*ln(a), we have: ln(6)/7 - 7*ln(x) - ln(y).

Learn more about Logarithm Properties