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

The solution to 2/5 log_{10}(m)+4log_{10}(n) is log_{10}(m^{2/5}n^4)

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

simplify

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

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

Solution steps

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

Apply log rule:

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

4 lo g_{10} (n) = lo g_{10} (n^{4})

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

ln (\frac{3 ^{x} 6 ^{2 x}}{2 ^{3 x}})

lo g_{5} (\frac{25}{x + 5})

ln (- 1) - ln (- 3)

lo g_{10} (100000 x x - 3)

lo g_{2} (5) - lo g_{2} (40)

What is 2/5 log_{10}(m)+4log_{10}(n) ?
The solution to 2/5 log_{10}(m)+4log_{10}(n) is log_{10}(m^{2/5}n^4)