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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (a e^{x}) + ln (b e^{- x})

ln (x d x)

ln (\frac{x ^{6}}{y ^{2}})

ln (c) + ln (a)

lo g_{5} (\frac{a ^{3}}{b ^{3}})

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