Use the properties of logarithms to expand the expression as

klytamnestra9a 2021-11-22 Answered
Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple of logarithms. (Assume the variable is positive.)
\(\displaystyle{\ln{{\left({\frac{{{x}}}{{\sqrt{{{x}^{{2}}+{1}}}}}}\right)}}}\)

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Expert Answer

Eprint
Answered 2021-11-23 Author has 489 answers
\(\displaystyle\text{logarithmic expression}{\ln{{\left({\frac{{{x}}}{{\sqrt{{{x}^{{2}}+{1}}}}}}\right)}}}\)
We know that,\(\displaystyle{\ln{{\left({\frac{{{a}}}{{{b}}}}\right)}}}={\log{{a}}}-{\log{{b}}}\)
\(\displaystyle{\ln{{\left({\frac{{{x}}}{{\sqrt{{{x}^{{2}}+{1}}}}}}\right)}}}\)
\(\displaystyle{\ln{{\left({x}\right)}}}-{\ln{{\left(\sqrt{{{x}^{{2}}+{1}}}\right)}}}\)
\(\displaystyle{\ln{{\left({x}\right)}}}-{{\ln{{\left(\sqrt{{{x}^{{2}}+{1}}}\right)}}}^{{\frac{{{1}}}{{{2}}}}}}\)
\(\displaystyle{\ln{{\left({x}\right)}}}-{\frac{{{1}}}{{{2}}}}{\ln{{\left({x}^{{2}}+{1}\right)}}}\)
\(\displaystyle\because{{\log{{a}}}^{{m}}=}{m}{\log{{a}}}\)
\(\displaystyle{\ln{{\left({x}\right)}}}-{\frac{{{1}}}{{{2}}}}{\ln{{\left({x}^{{2}}+{1}\right)}}}\)
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James Obrien
Answered 2021-11-24 Author has 1407 answers
Help me find a solution please, I just can't solve
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