What is 9log_{b}(x)+5log_{b}(z) ?

The solution to 9log_{b}(x)+5log_{b}(z) is log_{b}(x^9z^5)

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simplify 9log_{b}(x)+5log_{b}(z)

simplify

9 lo g_{b} (x) + 5 lo g_{b} (z)

lo g_{b} (x^{9} z^{5})

Solution steps

9 lo g_{b} (x) + 5 lo g_{b} (z)

Apply log rule:

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

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

= lo g_{b} (x^{9}) + 5 lo g_{b} (z)

Apply log rule:

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

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

= lo g_{b} (x^{9}) + lo g_{b} (z^{5})

Apply log rule:

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

lo g_{b} (x^{9}) + lo g_{b} (z^{5}) = lo g_{b} (x^{9} z^{5})

= lo g_{b} (x^{9} z^{5})

lo g_{10} (y) + 5 lo g_{10} (z)

lo g_{x} (\frac{7}{10})

- lo g_{10} (2.2 \cdot 1 0^{- 10})

lo g_{10} (x^{4})

lo g_{b} (\frac{p ^{2} q ^{7}}{m ^{4} b ^{9}})

What is 9log_{b}(x)+5log_{b}(z) ?
The solution to 9log_{b}(x)+5log_{b}(z) is log_{b}(x^9z^5)