What is 7log_{2}(u)+4log_{2}(v) ?

The solution to 7log_{2}(u)+4log_{2}(v) is log_{2}(u^7v^4)

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simplify 7log_{2}(u)+4log_{2}(v)

simplify

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

lo g_{2} (u^{7} v^{4})

Solution steps

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

Apply log rule:

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

7 lo g_{2} (u) = lo g_{2} (u^{7})

= lo g_{2} (u^{7}) + 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^{7}) + lo g_{2} (v^{4})

Apply log rule:

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

lo g_{2} (u^{7}) + lo g_{2} (v^{4}) = lo g_{2} (u^{7} v^{4})

= lo g_{2} (u^{7} v^{4})

ln (\frac{e ^{9}}{7})

lo g_{4} (8) + lo g_{4} (x)

lo g_{t} (6 t)

ln (\frac{2 \cdot e ^{- 1} + e ^{- 1} 1 + \frac{e ^{- 1} 1 ^{2}}{2}}{5})

lo g_{8} (\frac{8 x ^{4}}{y})

What is 7log_{2}(u)+4log_{2}(v) ?
The solution to 7log_{2}(u)+4log_{2}(v) is log_{2}(u^7v^4)