# Express 4ln(x)+2ln(x^4y^3)+5ln(z) as a single logarithm Our teacher has shown us examples for the same base and when it's both add and subtract. But I'm not sure how to do this.

Express $4\mathrm{ln}\left(x\right)+2\mathrm{ln}\left({x}^{4}{y}^{3}\right)+5\mathrm{ln}\left(z\right)$ as a single logarithm
Our teacher has shown us examples for the same base and when it's both add and subtract. But I'm not sure how to do this.
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moderrockblog09
Hint: $r\mathrm{ln}x=\mathrm{ln}\left({x}^{r}\right)$, so $4\mathrm{ln}\left(x\right)=\mathrm{ln}\left({x}^{4}\right)$. Also, $\mathrm{ln}\left(x\right)+\mathrm{ln}\left(y\right)+\mathrm{ln}\left(z\right)=\mathrm{ln}\left(xyz\right)$
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tarjetaroja2t
Hints:
$\mathrm{log}\left(x\right)+\mathrm{log}\left(y\right)=\mathrm{log}\left(xy\right)$ and $n\mathrm{log}\left(x\right)=log\left({x}^{n}\right)$ for logarithms of any base.