Armorikam

2021-08-18

Please, write the logarithm as a ratio of common logarithms and natural logarithms.

$\frac{{\mathrm{log}}_{1}}{4}\left(\u0445\right)$

a) common logarithms

b) natural logarithms

a) common logarithms

b) natural logarithms

Szeteib

Skilled2021-08-19Added 102 answers

a) Use the change-of-base formula using base 10

common logarithm:$\mathrm{log}}_{a}x=\frac{{\mathrm{log}}_{10}x}{{\mathrm{log}}_{10}\left(a\right)$

answer:$\mathrm{log}}_{\frac{1}{4}}x=\frac{{\mathrm{log}}_{10}x}{{\mathrm{log}}_{10}\left(\frac{1}{4}\right)$

b) Use the change-of-base formula using base e

natural logarithm:$\mathrm{log}}_{a}x=\frac{\mathrm{ln}x}{\mathrm{ln}a$

answer:$\mathrm{log}}_{\frac{1}{4}}x=\frac{\mathrm{ln}x}{\mathrm{ln}\left(\frac{1}{4}\right)$

common logarithm:

answer:

b) Use the change-of-base formula using base e

natural logarithm:

answer:

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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