What is 3log_{2}(u)+4log_{2}(v) ?

The solution to 3log_{2}(u)+4log_{2}(v) is log_{2}(u^3v^4)

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simplify 3log_{2}(u)+4log_{2}(v)

simplify

3 lo g_{2} (u) + 4 lo g_{2} (v)

lo g_{2} (u^{3} v^{4})

Solution steps

3 lo g_{2} (u) + 4 lo g_{2} (v)

Apply log rule:

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

3 lo g_{2} (u) = lo g_{2} (u^{3})

= lo g_{2} (u^{3}) + 4 lo g_{2} (v)

Apply log rule:

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

4 lo g_{2} (v) = lo g_{2} (v^{4})

= lo g_{2} (u^{3}) + lo g_{2} (v^{4})

Apply log rule:

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

lo g_{2} (u^{3}) + lo g_{2} (v^{4}) = lo g_{2} (u^{3} v^{4})

= lo g_{2} (u^{3} v^{4})

- lo g_{10} (3.16 \cdot 1 0^{- 7})

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

ln (3 x) - ln (\frac{1}{2} x)

lo g_{b} (\frac{x ^{3} y}{z ^{6}})

lo g_{2} (\frac{( x - 4 ) ^{2}}{x})

What is 3log_{2}(u)+4log_{2}(v) ?
The solution to 3log_{2}(u)+4log_{2}(v) is log_{2}(u^3v^4)