What is 9log_{b}(x)+3log_{b}(z) ?

The solution to 9log_{b}(x)+3log_{b}(z) is log_{b}(x^9z^3)

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simplify 9log_{b}(x)+3log_{b}(z)

simplify

9 lo g_{b} (x) + 3 lo g_{b} (z)

lo g_{b} (x^{9} z^{3})

Solution steps

9 lo g_{b} (x) + 3 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}) + 3 lo g_{b} (z)

Apply log rule:

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

3 lo g_{b} (z) = lo g_{b} (z^{3})

= lo g_{b} (x^{9}) + lo g_{b} (z^{3})

Apply log rule:

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

lo g_{b} (x^{9}) + lo g_{b} (z^{3}) = lo g_{b} (x^{9} z^{3})

= lo g_{b} (x^{9} z^{3})

lo g_{5} (\frac{( x ^{2} )}{y ^{2} z ^{3}})

lo g_{6} (11) - lo g_{6} (z)

lo g_{9} (\frac{3 a}{7})

\frac{ln ( \frac{5}{3} )}{ln ( 3 ) - ln ( 5 )}

- 2 ln (3) + 3 ln (4) + 3 ln (2)

What is 9log_{b}(x)+3log_{b}(z) ?
The solution to 9log_{b}(x)+3log_{b}(z) is log_{b}(x^9z^3)