Question

Help expanding natural logarithms please?

ln2x/ln6y

Answer 1

you can write ln(2x) as ln(2) + ln(x)
you can use the same idea for ln 6y

Answer 2

ok so i would get ln(2)+ln(x)/ ln(6)+ln(y)
and then would i subtract the bottom from the top and write it as: ln(2)+ln(x)-ln(6)-ln(y) ?

Answer 3

@phi

Answer 4

\[(\ln2x)/(\ln6y)=\frac{ \ln 2 +\ln x }{ \ln 6+\ln x }\]

Answer 5

You cannot take this any further.

Your question pertains to \[\ln \frac{ 2x }{ 6y }=\ln \frac{ x }{ 3y }=\ln x - (\ln 3 + \ln y)\]

Answer 6

which is an entirely different problem in logs.