Question

expand : ln(2y/x)

Answer 1

Division of terms within a logarithm means you can create a subtraction of two logarithms, one with each of thefractional terms. Multiplication of things inside of a logarithm meansyou can expand into an addition of those two products. So this problem can expand into 3 ln's. Two from the splitting of 2y / x and the 3rd from the splitting of 2 and y.

Answer 2

\[\ln \left( \frac{ a }{ b } \right)=\ln a-\ln b\] and
\[\ln \left( ab \right)=\ln a +\ln b\]
Use these to rewrite (expand) the given.

Answer 3

ln 2+ln y-ln x