What is 4log_{b}(x)+5log_{b}(z) ?

The solution to 4log_{b}(x)+5log_{b}(z) is log_{b}(x^4z^5)

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simplify 4log_{b}(x)+5log_{b}(z)

simplify

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

lo g_{b} (x^{4} z^{5})

Solution steps

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

Apply log rule:

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

4 lo g_{b} (x) = lo g_{b} (x^{4})

= lo g_{b} (x^{4}) + 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^{4}) + lo g_{b} (z^{5})

Apply log rule:

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

lo g_{b} (x^{4}) + lo g_{b} (z^{5}) = lo g_{b} (x^{4} z^{5})

= lo g_{b} (x^{4} z^{5})

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

lo g_{4} (9 x)

lo g_{10} (\frac{x y ^{5}}{z ^{5}})

lo g_{10} (x^{2} \frac{x + 3}{x - 1})

\frac{1}{2} lo g_{3} (9 x) + \frac{3}{2} lo g_{3} (4 x^{3})

What is 4log_{b}(x)+5log_{b}(z) ?
The solution to 4log_{b}(x)+5log_{b}(z) is log_{b}(x^4z^5)