What is 6log_{10}(m)-2log_{10}(n) ?

The solution to 6log_{10}(m)-2log_{10}(n) is log_{10}((m^6)/(n^2))

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simplify 6log_{10}(m)-2log_{10}(n)

simplify

6 lo g_{10} (m) - 2 lo g_{10} (n)

lo g_{10} (\frac{m ^{6}}{n ^{2}})

Solution steps

6 lo g_{10} (m) - 2 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}) - 2 lo g_{10} (n)

Apply log rule:

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

2 lo g_{10} (n) = lo g_{10} (n^{2})

= lo g_{10} (m^{6}) - lo g_{10} (n^{2})

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^{2}) = lo g_{10} (\frac{m ^{6}}{n ^{2}})

= lo g_{10} (\frac{m ^{6}}{n ^{2}})

- lo g_{10} (9.1 \cdot 1 0^{- 13})

\frac{ln ( 2 )}{ln ( 2 ) - ln ( 3 )}

ln (a^{2} b^{3})

- ln (x) - ln (3) + ln (6)

0.5 lo g_{b} (x + 7) - lo g_{b} (x - 3)

What is 6log_{10}(m)-2log_{10}(n) ?
The solution to 6log_{10}(m)-2log_{10}(n) is log_{10}((m^6)/(n^2))