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

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

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simplify log_{10}(m/(10n))

simplify

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

lo g_{10} (m) - 1 - lo g_{10} (n)

Solution steps

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

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

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

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

Simplify

lo g_{10} (10 n) : 1 + lo g_{10} (n)

= lo g_{10} (m) - (1 + lo g_{10} (n))

Apply the distributive law:

- (a + b) = - a - b

- (1 + lo g_{10} (n)) = - 1 - lo g_{10} (n)

= lo g_{10} (m) - 1 - lo g_{10} (n)

lo g_{10} (3 x y^{3})

ln (12) + ln (3)

ln (\frac{( 3 y + 1 ) ^{4}}{y ^{2} + 1})

ln (x (x + 3))

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