What is 4log_{10}(m)-log_{10}(n) ?

The solution to 4log_{10}(m)-log_{10}(n) is log_{10}((m^4)/n)

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simplify 4log_{10}(m)-log_{10}(n)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3 lo g_{7} (a) - lo g_{7} (b)

ln (\frac{1}{2 \cdot π \cdot det ( x )})

ln (\frac{e}{e + 1}) - ln (\frac{1}{2})

ln (x) + ln (x^{2} - 1)

ln (\frac{22.4}{10.1})

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