What is 6log_{b}(x)+9log_{b}(z) ?

The solution to 6log_{b}(x)+9log_{b}(z) is log_{b}(x^6z^9)

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simplify 6log_{b}(x)+9log_{b}(z)

simplify

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

lo g_{b} (x^{6} z^{9})

Solution steps

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

Apply log rule:

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

6 lo g_{b} (x) = lo g_{b} (x^{6})

= lo g_{b} (x^{6}) + 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^{6}) + lo g_{b} (z^{9})

Apply log rule:

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

lo g_{b} (x^{6}) + lo g_{b} (z^{9}) = lo g_{b} (x^{6} z^{9})

= lo g_{b} (x^{6} z^{9})

lo g_{2} (4 x^{2})

ln (\frac{k ^{3}}{m ^{8}})

ln (x^{7} - 1) - ln (x^{5} - 1)

lo g_{3} (\frac{27 b ^{3} y ^{2} - 1}{y ( x + 1 ) ^{2}})

\frac{1}{20} ln (2)

What is 6log_{b}(x)+9log_{b}(z) ?
The solution to 6log_{b}(x)+9log_{b}(z) is log_{b}(x^6z^9)