Is the above formatted equation true or false when dealing with logarithms.

It appears what you're trying to ask is whether this is true:


ln(x+3) - ln(2x) = \frac {ln(x+3)}{ln(2x)}


No these are not equaivalent. But the following IS true:


ln(x+3) - ln(2x) = ln (\frac {x+3}{2x} )


The principals to remember are: ln(a x b ) = ln(a) + ln(b), and ln(a/b) = ln(a) - ln(b).