What is 10log_{9}(w)+8log_{9}(x) ?

The solution to 10log_{9}(w)+8log_{9}(x) is log_{9}(w^{10}x^8)

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simplify 10log_{9}(w)+8log_{9}(x)

simplify

10 lo g_{9} (w) + 8 lo g_{9} (x)

lo g_{9} (w^{10} x^{8})

Solution steps

10 lo g_{9} (w) + 8 lo g_{9} (x)

Apply log rule:

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

10 lo g_{9} (w) = lo g_{9} (w^{10})

= lo g_{9} (w^{10}) + 8 lo g_{9} (x)

Apply log rule:

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

8 lo g_{9} (x) = lo g_{9} (x^{8})

= lo g_{9} (w^{10}) + lo g_{9} (x^{8})

Apply log rule:

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

lo g_{9} (w^{10}) + lo g_{9} (x^{8}) = lo g_{9} (w^{10} x^{8})

= lo g_{9} (w^{10} x^{8})

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What is 10log_{9}(w)+8log_{9}(x) ?
The solution to 10log_{9}(w)+8log_{9}(x) is log_{9}(w^{10}x^8)