# Write each expression as a single natural logarithm. 2ln 8-3ln 4

Write each expression as a single natural logarithm. $2\mathrm{ln}8-3\mathrm{ln}4$
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stuth1
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: $\mathrm{ln}\frac{m}{n}=\mathrm{ln}m-\mathrm{ln}n$
$=\mathrm{ln}\frac{64}{64}=\mathrm{ln}1$
Note that $\mathrm{ln}1=0$ but since we are asked to write as a single natural logarithm, then we leave the answer as is $\mathrm{ln}1=0$