What is 1/2 log_{10}(n)+3log_{10}(m) ?

The solution to 1/2 log_{10}(n)+3log_{10}(m) is log_{10}(n^{1/2}m^3)

Popular >

simplify 1/2 log_{10}(n)+3log_{10}(m)

simplify

\frac{1}{2} lo g_{10} (n) + 3 lo g_{10} (m)

lo g_{10} (n^{\frac{1}{2}} m^{3})

Solution steps

\frac{1}{2} lo g_{10} (n) + 3 lo g_{10} (m)

Apply log rule:

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

\frac{1}{2} lo g_{10} (n) = lo g_{10} (n^{\frac{1}{2}})

= lo g_{10} (n^{\frac{1}{2}}) + 3 lo g_{10} (m)

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} (n^{\frac{1}{2}}) + lo g_{10} (m^{3})

Apply log rule:

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

lo g_{10} (n^{\frac{1}{2}}) + lo g_{10} (m^{3}) = lo g_{10} (m^{3} n^{\frac{1}{2}})

= lo g_{10} (n^{\frac{1}{2}} m^{3})

lo g_{u} (u^{- 7}) + 5 lo g_{u} (u^{\frac{2}{5}})

lo g_{2} (5) + lo g_{2} (6)

lo g_{b} (\frac{1.792}{1.946})

\frac{1}{4} lo g_{5} (16) + \frac{1}{5} lo g_{5} (243)

4 ln (x) + 6 ln (y) - 3 ln (z)

What is 1/2 log_{10}(n)+3log_{10}(m) ?
The solution to 1/2 log_{10}(n)+3log_{10}(m) is log_{10}(n^{1/2}m^3)