What is 8log_{b}(x)+7log_{b}(z) ?

The solution to 8log_{b}(x)+7log_{b}(z) is log_{b}(x^8z^7)

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simplify 8log_{b}(x)+7log_{b}(z)

simplify

8 lo g_{b} (x) + 7 lo g_{b} (z)

lo g_{b} (x^{8} z^{7})

Solution steps

8 lo g_{b} (x) + 7 lo g_{b} (z)

Apply log rule:

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

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

= lo g_{b} (x^{8}) + 7 lo g_{b} (z)

Apply log rule:

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

7 lo g_{b} (z) = lo g_{b} (z^{7})

= lo g_{b} (x^{8}) + lo g_{b} (z^{7})

Apply log rule:

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

lo g_{b} (x^{8}) + lo g_{b} (z^{7}) = lo g_{b} (x^{8} z^{7})

= lo g_{b} (x^{8} z^{7})

\frac{π}{8} ln (\frac{13}{5})

- [\frac{2}{6} lo g_{2} (\frac{2}{6}) + \frac{4}{6} lo g_{2} (\frac{4}{6})]

3 lo g_{b} (q) - lo g_{b} (r)

lo g_{2} ((3^{6} \cdot 7)^{4})

\frac{1}{2} lo g_{10} (261)

What is 8log_{b}(x)+7log_{b}(z) ?
The solution to 8log_{b}(x)+7log_{b}(z) is log_{b}(x^8z^7)