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In a book it states $\ln(2e^2)$ is the same as $\ln(2\cdot 2^2)=\ln8$.

When I reduce the expression $\ln(2e^2)$, I get the result $\ln2+2$. This seems right, since you use logarithm rule $\log(ab)=\log a+\log b$, so you get $$\ln 2+\ln e^2=\ln 2+2\ln e=\ln2+2\cdot 1=\ln 2+2$$

But why in the world would the book write the answer as $\ln(2\cdot 2^2)=\ln 8$?

It has no logical explanation for me, help!

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Vladimir Civilgin
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    $\ln \left( 2\times e^2\right)$ is clearly not the same as $\ln \left(2 \times 2^2\right)$. If your text actually says this, then they have made a mistake. – lulu Oct 09 '19 at 23:33
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    Every math book have some mistakes in it and they often post them online if there is a mistake but i couldn´t find any, thats why i thought that it´s maybe just me that is mistaken, but my equations was right. Thank you for clearifying :) – Vladimir Civilgin Oct 09 '19 at 23:38
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    Please name the book. That would make your question and the comments and answers much more useful to other MSE users. – Rob Arthan Oct 10 '19 at 00:12

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