What is 3log_{10}(m)+2/3 log_{10}(n) ?

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

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simplify 3log_{10}(m)+2/3 log_{10}(n)

simplify

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

lo g_{10} (m^{3} n^{\frac{2}{3}})

Solution steps

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

Apply log rule:

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

3 lo g_{10} (m) = lo g_{10} (m^{3})

= lo g_{10} (m^{3}) + \frac{2}{3} lo g_{10} (n)

Apply log rule:

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

\frac{2}{3} lo g_{10} (n) = lo g_{10} (n^{\frac{2}{3}})

= lo g_{10} (m^{3}) + lo g_{10} (n^{\frac{2}{3}})

Apply log rule:

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

lo g_{10} (m^{3}) + lo g_{10} (n^{\frac{2}{3}}) = lo g_{10} (m^{3} n^{\frac{2}{3}})

= lo g_{10} (m^{3} n^{\frac{2}{3}})

lo g_{8} (9 x)

lo g_{3} (6) + lo g_{3} (c)

3.8 + lo g_{10} (1.77 \times 1 0^{- 4})

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