What is 1/3 log_{10}(m)-2log_{10}(n) ?

The solution to 1/3 log_{10}(m)-2log_{10}(n) is log_{10}((m^{1/3})/(n^2))

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simplify 1/3 log_{10}(m)-2log_{10}(n)

simplify

\frac{1}{3} lo g_{10} (m) - 2 lo g_{10} (n)

lo g_{10} (\frac{m ^{\frac{1}{3}}}{n ^{2}})

Solution steps

\frac{1}{3} lo g_{10} (m) - 2 lo g_{10} (n)

Apply log rule:

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

\frac{1}{3} lo g_{10} (m) = lo g_{10} (m^{\frac{1}{3}})

= lo g_{10} (m^{\frac{1}{3}}) - 2 lo g_{10} (n)

Apply log rule:

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

2 lo g_{10} (n) = lo g_{10} (n^{2})

= lo g_{10} (m^{\frac{1}{3}}) - lo g_{10} (n^{2})

Apply log rule:

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

lo g_{10} (m^{\frac{1}{3}}) - lo g_{10} (n^{2}) = lo g_{10} (\frac{m ^{\frac{1}{3}}}{n ^{2}})

= lo g_{10} (\frac{m ^{\frac{1}{3}}}{n ^{2}})

ln (\frac{( x ^{2} - 5 x + 3 ) ( x - 5 ) ^{5}}{( 3 x ^{2} + 2 ) ^{6}})

20 e^{9} + ln (12) + 50 + ln (9)

4 lo g_{10} (x) + 3 lo g_{10} (y) - 2 lo g_{10} (z)

3 ln (\frac{a}{2}) + 2 ln (2 b)

What is 1/3 log_{10}(m)-2log_{10}(n) ?
The solution to 1/3 log_{10}(m)-2log_{10}(n) is log_{10}((m^{1/3})/(n^2))