What is 5log_{b}(w)+2log_{b}(v) ?

The solution to 5log_{b}(w)+2log_{b}(v) is log_{b}(w^5v^2)

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simplify 5log_{b}(w)+2log_{b}(v)

simplify

5 lo g_{b} (w) + 2 lo g_{b} (v)

lo g_{b} (w^{5} v^{2})

Solution steps

5 lo g_{b} (w) + 2 lo g_{b} (v)

Apply log rule:

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

5 lo g_{b} (w) = lo g_{b} (w^{5})

= lo g_{b} (w^{5}) + 2 lo g_{b} (v)

Apply log rule:

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

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

= lo g_{b} (w^{5}) + lo g_{b} (v^{2})

Apply log rule:

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

lo g_{b} (w^{5}) + lo g_{b} (v^{2}) = lo g_{b} (w^{5} v^{2})

= lo g_{b} (w^{5} v^{2})

ln (\frac{55.1}{760})

ln (sec (\frac{π}{3})) + 1 + ln (c) + ln (\frac{π}{4})

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

ln (2 x^{2} - 2 x) + ln (\frac{1}{2 x})

ln ∣ vx ∣ - ln ∣ v ∣

What is 5log_{b}(w)+2log_{b}(v) ?
The solution to 5log_{b}(w)+2log_{b}(v) is log_{b}(w^5v^2)