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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (3) + 2 ln (x) - 9 ln (y)

ln (\frac{r}{s})

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

3 ln ∣ 5 ∣ - 3 ln ∣ 2 ∣

ln (2 u)

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