Please, write the logarithm as a ratio of common logarithms

Armorikam 2021-08-18 Answered
Please, write the logarithm as a ratio of common logarithms and natural logarithms.
\(\displaystyle\frac{{\log}_{{1}}}{{4}}{\left(х\right)}\)
a) common logarithms
b) natural logarithms

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

Szeteib
Answered 2021-08-19 Author has 5839 answers
a) Use the change-of-base formula using base 10
common logarithm: \(\displaystyle{{\log}_{{a}}{x}}={\frac{{{{\log}_{{10}}{x}}}}{{{{\log}_{{10}}{\left({a}\right)}}}}}\)
answer: \(\displaystyle{{\log}_{{\frac{{1}}{{4}}}}{x}}={\frac{{{{\log}_{{10}}{x}}}}{{{{\log}_{{10}}{\left(\frac{{1}}{{4}}\right)}}}}}\)
b) Use the change-of-base formula using base e
natural logarithm: \(\displaystyle{{\log}_{{a}}{x}}={\frac{{{\ln{{x}}}}}{{{\ln{{a}}}}}}\)
answer: \(\displaystyle{{\log}_{{\frac{{1}}{{4}}}}{x}}={\frac{{{\ln{{x}}}}}{{{\ln{{\left(\frac{{1}}{{4}}\right)}}}}}}\)
Have a similar question?
Ask An Expert
1
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-08-21
Please, write the logarithm as a ratio of common logarithms and natural logarithms.
\(\displaystyle{{\log}_{{x}}{\left(\frac{{3}}{{10}}\right)}}\)
a) common logarithms
b) natural logarithms
asked 2021-08-10
Please, write the logarithm as a ratio of common logarithms and natural logarithms.
\(\displaystyle{{\log}_{{x}}{\left(\frac{{3}}{{7}}\right)}}\)
a) common logarithms
b) natural logarithms
asked 2021-08-14
Please, write the logarithm as a ratio of common logarithms and natural logarithms.
\(\displaystyle{{\log}_{{9}}{\left({69}\right)}}\)
a) common logarithms
b) natural logarithms
asked 2021-08-13
Please, write the logarithm as a ratio of common logarithms and natural logarithms.
\(\displaystyle\frac{{\log}_{{1}}}{{7}}{\left({4}\right)}\)
a) common logarithms
b) natural logarithms
asked 2021-08-19
Rewrite the logarithm as a ratio of common logarithms and natural ones. \(\displaystyle{{\log}_{{x}}{\left(\frac{{3}}{{7}}\right)}}\)
asked 2021-08-18
Please, write the logarithm as a ratio of common logarithms and natural logarithms.
\(\displaystyle{{\log}_{{8}}{\left({51}\right)}}\)
a) common logarithms
b) natural logarithms
asked 2021-08-19
Please, write the logarithm as a ratio of common logarithms and natural logarithms.
\(\displaystyle{{\log}_{{5}}{\left({86}\right)}}\)
a) common logarithms
b) natural logarithms
...