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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

3 lo g_{10} (n) = lo g_{10} (n^{3})

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

Apply log rule:

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

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

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

lo g_{9} (\frac{f}{81})

ln (\frac{5}{7 x ^{7} y})

\frac{1}{2} ln (\frac{cos ( x ) - 1}{cos ( x ) + 1})

ln (\frac{7}{6}) + ln (\frac{5}{6})

9 ln (x + 3) - 2 ln (x)

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