foass77W

2021-08-10

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

${\mathrm{log}}_{x}\left(\frac{3}{7}\right)$

a) common logarithms

b) natural logarithms

a) common logarithms

b) natural logarithms

Leonard Stokes

Skilled2021-08-11Added 98 answers

common logarithms, here we take to the base 10

$\mathrm{log}}_{b}a=\frac{\mathrm{log}\left(a\right)}{\mathrm{log}\left(b\right)$

$\mathrm{log}}_{x}\left(\frac{3}{7}\right)=\frac{\mathrm{log}\left(\frac{3}{7}\right)}{\mathrm{log}\left(x\right)$

natural logarithms, here we take to the base e

$\mathrm{log}}_{b}a=\frac{\mathrm{ln}\left(a\right)}{\mathrm{ln}\left(b\right)$

$\mathrm{log}}_{x}\left(\frac{3}{7}\right)=\frac{\mathrm{ln}\left(\frac{3}{7}\right)}{\mathrm{ln}\left(x\right)$

natural logarithms, here we take to the base e

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

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