 Recent questions in Logarithms
Logarithms
ANSWERED ### Find 1.8x, if $$\displaystyle{e}^{{{1.8}{x}}}={2}.$$

Logarithms
ANSWERED ### 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

Logarithms
ANSWERED ### Use the properties of logarithms to write expression as a sum, difference, or product of simpler logarithms. $$\ln \frac{2\sqrt{5}}{\sqrt{7}}$$

Logarithms
ANSWERED ### Please, write the logarithm as a ratio of common logarithms and natural logarithms. $$\displaystyle\frac{{\log}_{{1}}}{{5}}{\left({4}\right)}$$ a) common logarithms b) natural logarithms

Logarithms
ANSWERED ### Solve $$\displaystyle{\left({\log{{\left({7}{x}\right)}}}\right)}{\log{{x}}}={5}$$

Logarithms
ANSWERED ### Rewrite the logarithm as a ratio of common logarithms and natural ones. $$\displaystyle{{\log}_{{x}}{\left(\frac{{3}}{{7}}\right)}}$$

Logarithms
ANSWERED ### 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

Logarithms
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

Logarithms
ANSWERED ### 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

Logarithms
ANSWERED ### Using the change-of-base formula, evaluate the logarithm. Round your result to three decimal places. $$\displaystyle{{\log}_{{36}}{\left({25}\right)}}$$

Logarithms
ANSWERED ### Please, write the logarithm as a ratio of common logarithms and natural logarithms. $$\displaystyle{{\log}_{{3}}{\left({x}\right)}}$$ a) common logarithms b) natural logarithms

Logarithms
ANSWERED ### Examine whether the series $$\sum_{n=2}^\infty \frac{1}{(\log n)^{\log n}}$$ is convergent. $$\displaystyle{n}={2}$$

Logarithms
ANSWERED ### Please, write the logarithm as a ratio of common logarithms and natural logarithms. $$\displaystyle{{\log}_{{4}}{\left({71}\right)}}$$ a) common logarithms b) natural logarithms

Logarithms
ANSWERED ### Evaluate the maximum rate of change of $$\displaystyle{f{{\left({x},{y}\right)}}}={\ln{{\left({x}^{{2}}+{y}^{{2}}\right)}}}$$ at the point (3,2) and the direction in which it occurs. What is maximum rate of change and direction(unit vector) in which it occurs?

Logarithms
ANSWERED ### Most textbooks in calculus and the sciences, as well as calculators, use the notation ln x for the natural logarithm and log x for the “common logarithm,” $$\displaystyle{{\log}_{{{10}}}{\left\lbrace{x}\right\rbrace}}$$. In the more advanced mathematical and scientific literature and in computer languages, however, the notation log x usually denotes the natural logarithm.

Logarithms
ANSWERED ### Write the following logarithms in terms of the natural logarithm. Then use a calculator to find the value of the logarithm, rounding your result to four decimal places. $$\displaystyle{{\log}_{{{4}}}{\left\lbrace{40}\right\rbrace}}$$

Logarithms
ANSWERED ### $$\displaystyle{5}{\left({10}^{{x}}−{6}\right)}={7}$$

Logarithms
ANSWERED ### 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

Logarithms
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