What is 2/5 log_{10}(m)-3/4 log_{10}(n) ?

The solution to 2/5 log_{10}(m)-3/4 log_{10}(n) is log_{10}((m^{2/5}\sqrt[4]{n})/n)

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simplify 2/5 log_{10}(m)-3/4 log_{10}(n)

simplify

\frac{2}{5} lo g_{10} (m) - \frac{3}{4} lo g_{10} (n)

Solution steps

\frac{2}{5} lo g_{10} (m) - \frac{3}{4} lo g_{10} (n)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{2}{5} lo g_{10} (m) = lo g_{10} (m^{\frac{2}{5}})

= lo g_{10} (m^{\frac{2}{5}}) - \frac{3}{4} lo g_{10} (n)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{3}{4} lo g_{10} (n) = lo g_{10} (n^{\frac{3}{4}})

= lo g_{10} (m^{\frac{2}{5}}) - lo g_{10} (n^{\frac{3}{4}})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (m^{\frac{2}{5}}) - lo g_{10} (n^{\frac{3}{4}}) = lo g_{10} (\frac{m ^{\frac{2}{5}}}{n ^{\frac{3}{4}}})

= lo g_{10} (\frac{m ^{\frac{2}{5}}}{n ^{\frac{3}{4}}})

Simplify

lo g_{4} (7) - lo g_{4} (\frac{8}{5})

ln (7 e^{7 x})

lo g_{10} (x^{2}) (x + 4)

lo g_{10} (\frac{x ( x + 3 )}{( x + 5 ) ^{9}})

What is 2/5 log_{10}(m)-3/4 log_{10}(n) ?
The solution to 2/5 log_{10}(m)-3/4 log_{10}(n) is log_{10}((m^{2/5}\sqrt[4]{n})/n)