What is 6log_{10}(m)-6log_{10}(n) ?

The solution to 6log_{10}(m)-6log_{10}(n) is log_{10}((m^6)/(n^6))

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simplify 6log_{10}(m)-6log_{10}(n)

simplify

6 lo g_{10} (m) - 6 lo g_{10} (n)

lo g_{10} (\frac{m ^{6}}{n ^{6}})

Solution steps

6 lo g_{10} (m) - 6 lo g_{10} (n)

Apply log rule:

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

6 lo g_{10} (m) = lo g_{10} (m^{6})

= lo g_{10} (m^{6}) - 6 lo g_{10} (n)

Apply log rule:

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

6 lo g_{10} (n) = lo g_{10} (n^{6})

= lo g_{10} (m^{6}) - lo g_{10} (n^{6})

Apply log rule:

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

lo g_{10} (m^{6}) - lo g_{10} (n^{6}) = lo g_{10} (\frac{m ^{6}}{n ^{6}})

= lo g_{10} (\frac{m ^{6}}{n ^{6}})

- 0.1386 \cdot ln (\frac{523}{298}) - 0.19867

8.314 \cdot ln (\frac{15000}{2000})

ln (\frac{e}{8})

lo g_{10} (a b^{2} c)

ln (x e^{(\frac{y}{z})})

What is 6log_{10}(m)-6log_{10}(n) ?
The solution to 6log_{10}(m)-6log_{10}(n) is log_{10}((m^6)/(n^6))