What is expand log_{10}((8m)/n) ?

The solution to expand log_{10}((8m)/n) is 3log_{10}(2)+log_{10}(m)-log_{10}(n)

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expand log_{10}((8m)/n)

expand

lo g_{10} (\frac{8 m}{n})

3 lo g_{10} (2) + lo g_{10} (m) - lo g_{10} (n)

Solution steps

lo g_{10} (\frac{8 m}{n})

Apply log rule:

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

lo g_{10} (\frac{8 m}{n}) = lo g_{10} (8 m) - lo g_{10} (n)

= lo g_{10} (8 m) - lo g_{10} (n)

Apply log rule:

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

lo g_{10} (8 m) = lo g_{10} (8) + lo g_{10} (m)

= lo g_{10} (8) + lo g_{10} (m) - lo g_{10} (n)

lo g_{10} (8) = 3 lo g_{10} (2)

= 3 lo g_{10} (2) + lo g_{10} (m) - lo g_{10} (n)

lo g_{9} (k^{2} - 81) - lo g_{9} (k) - 9

2 lo g_{10} (u) - 3 lo g_{10} (v) - 2 lo g_{10} (z)

lo g_{2} (7) + lo g_{2} (3)

ln (\frac{( x y ) ^{2}}{z ^{3}})

9 ln (t) + ln (y) - ln (y + 1)

What is expand log_{10}((8m)/n) ?
The solution to expand log_{10}((8m)/n) is 3log_{10}(2)+log_{10}(m)-log_{10}(n)