Braxton Pugh

2021-03-02

Write each expression as a single natural logarithm. $2\mathrm{ln}8-3\mathrm{ln}4$

stuth1

Skilled2021-03-03Added 97 answers

Apply Power Property: $\mathrm{ln}{m}^{n}=n\mathrm{ln}m$

$=\mathrm{ln}{8}^{2}-\mathrm{ln}{4}^{3}$

$=\mathrm{ln}64-\mathrm{ln}64$

Apply Quotient Property: $\mathrm{ln}\frac{m}{n}=\mathrm{ln}m-\mathrm{ln}n$

$=\mathrm{ln}\frac{64}{64}=\mathrm{ln}1$

Recall that $\mathrm{ln}1=0$. However, since we must express the answer as a single natural logarithm, we leave the response as is $\mathrm{ln}1=0$

2022-03-11

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