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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{1}{2} lo g_{c} (x) + 2 lo g_{c} (y) - 3 lo g_{c} (x)

- lo g_{10} (1.9 \cdot 1 0^{- 6})

lo g_{3} (x^{2} - 25) - lo g_{3} (x - 5)

lo g_{5} (\frac{c}{25})

x y + ln (\frac{x}{e})

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