Question

what does it mean when a problem says "in terms of" example Express the following logarithm as specified . Natural log Root 40.5 in terms of natural log 3 and natural log 4. Thank you in advance for your help.

Answer 1

By natural log 3, do you mean \(\log_{e}(3)=\ln(3)\) ?

Answer 2

in terms of,
meaning the answer will be exclusively expressed in those tems

Answer 3

thus ... far all I've found is ... \(\bf ln(\sqrt{40.5}) \implies ln\left(40.5^{\frac{1}{2}}\right) \implies \cfrac{1}{2}ln(40.5) \implies \cfrac{ln(40.5)}{2}\\\qquad \\
\textit{now we can say that } 40.5 = 3^2 \times 4.5 \textit{thus}\\
\qquad \\
\cfrac{ln(40.5)}{2} \implies \cfrac{ln(3^2 \times 4.5)}{2} \implies \cfrac{ln(3^2) + ln(4.5)}{2}\\ \implies \cfrac{2ln(3) + ln(4.5)}{2} \implies ln(3) + \cfrac{ln(4.5)}{2}\)

Answer 4

For some reason my computer is having difficulties in rendering LaTex just give me a moment.

Answer 5

@KeithAfasCalcLover try maybe at http://mathb.in/ it has better latency

Answer 6

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