I am studying for a math competition at my school and this here just stumps me.

$\displaystyle \textrm{ln}\frac{3x^4}{5y^2}$

My work:

Quotient property:

$\displaystyle \textrm{ln}3x^4-\textrm{ln}5y^2$

Power property:

$\displaystyle 4\textrm{ln}3x-2\textrm{ln}5y$

Product property:

$\displaystyle \textrm{ln}3+4\textrm{ln}x-\textrm{ln}5+2\textrm{ln}y$

And this is what I have got after a long time of trying...

But the answer key says the answer is:

$\displaystyle \textrm{ln}3+4\textrm{ln}x-\textrm{ln}5-2\textrm{ln}y$

can someone explain this to me?

thanks.

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