The solution is written below

asked 2021-11-14

Use the properties of logarithms to write expression as a sum, difference, or product of simpler logarithms.

\(\displaystyle{{\log}_{{5}}{\left({2}{k}\right)}}\)

\(\displaystyle{{\log}_{{5}}{\left({2}{k}\right)}}\)

asked 2021-02-18

asked 2021-02-25

Write \(\log_3 \frac{1}{27x^{2}}\) in the form a+b \(\log_3x\) where a and b are integers

asked 2021-11-08

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expression

\(\displaystyle{8}{\ln{{x}}}-{\frac{{{1}}}{{{3}}}}{\ln{{y}}}\)

\(\displaystyle{8}{\ln{{x}}}-{\frac{{{1}}}{{{3}}}}{\ln{{y}}}\)

asked 2021-08-10

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator.

\(\displaystyle{\frac{{{1}}}{{{3}}}}{\left({{\log}_{{{4}}}{\left\lbrace{x}\right\rbrace}}-{{\log}_{{{4}}}{\left\lbrace{y}\right\rbrace}}\right)}\)

\(\displaystyle{\frac{{{1}}}{{{3}}}}{\left({{\log}_{{{4}}}{\left\lbrace{x}\right\rbrace}}-{{\log}_{{{4}}}{\left\lbrace{y}\right\rbrace}}\right)}\)

asked 2021-11-22

Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple of logarithms. (Assume the variable is positive.)

\(\displaystyle{\ln{{\left({\frac{{{x}}}{{\sqrt{{{x}^{{2}}+{1}}}}}}\right)}}}\)

\(\displaystyle{\ln{{\left({\frac{{{x}}}{{\sqrt{{{x}^{{2}}+{1}}}}}}\right)}}}\)

asked 2021-11-08

Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calculator.

\(\displaystyle{{\log}_{{4}}{\left({48}{x}+{16}{y}\right)}}\)

\(\displaystyle{{\log}_{{4}}{\left({48}{x}+{16}{y}\right)}}\)