FobelloE

2021-10-21

Write the following expression as a sum and/or diffence of logarithm.Express powers as factors.

$\mathrm{ln}\left\{\frac{x}{{e}^{x}}\right\}$

Willie

Skilled2021-10-22Added 95 answers

Step 1

given that$\mathrm{ln}\frac{x}{{e}^{x}}$

We need to express the given expression as a sum or difference of logarithms. Let$y=\mathrm{ln}\frac{x}{{e}^{x}}$

according to logaritm property$\mathrm{ln}\frac{m}{n}=\mathrm{ln}\left(m\right)-\mathrm{ln}\left(n\right)$ So

$y=\mathrm{ln}x-{\mathrm{ln}e}^{x}$

we know that${\mathrm{ln}e}^{x}=x$

So

$y=\mathrm{ln}x-x$

given that

We need to express the given expression as a sum or difference of logarithms. Let

according to logaritm property

we know that

So

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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