Condense the expression to the logarithm of a single quantity.
5lnx-6ln(x+2)
5lnx-6ln(x+2)
ln x^5 - ln (x-2)^6
ln [x^5/(x-2)^6]
To condense the expression to the logarithm of a single quantity, we can use the properties of logarithms. Specifically, we can use the product rule and the quotient rule of logarithms.
First, let's rewrite the expression using the properties of logarithms:
5ln(x) - 6ln(x+2)
Now let's apply the product rule, which states that ln(a) + ln(b) = ln(a*b), and the quotient rule, which states that ln(a) - ln(b) = ln(a/b):
5ln(x) - 6ln(x+2) = ln(x^5) - ln((x+2)^6)
Using the quotient rule, we can rewrite this expression as the quotient of two logarithms:
ln(x^5/(x+2)^6)
So, the condensed expression is:
ln(x^5/(x+2)^6)