What is 5log_{b}(x)+2log_{b}(z) ?

The solution to 5log_{b}(x)+2log_{b}(z) is log_{b}(x^5z^2)

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simplify 5log_{b}(x)+2log_{b}(z)

simplify

5 lo g_{b} (x) + 2 lo g_{b} (z)

lo g_{b} (x^{5} z^{2})

Solution steps

5 lo g_{b} (x) + 2 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}) + 2 lo g_{b} (z)

Apply log rule:

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

2 lo g_{b} (z) = lo g_{b} (z^{2})

= lo g_{b} (x^{5}) + lo g_{b} (z^{2})

Apply log rule:

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

lo g_{b} (x^{5}) + lo g_{b} (z^{2}) = lo g_{b} (x^{5} z^{2})

= lo g_{b} (x^{5} z^{2})

2 lo g_{x} (- 4 lo g_{y} (x))

\frac{1}{2} lo g_{10} (6)

ln (\frac{2.3113 \cdot 1 0 ^{- 1}}{4.98 \cdot 1 0 ^{- 3}})

\frac{1}{4} ln \frac{3}{2} - \frac{2}{1} - \frac{1}{4} ln \frac{3}{2} + \frac{2}{1}

lo g_{2} (x - 5) + lo g_{2} (x - 11)

What is 5log_{b}(x)+2log_{b}(z) ?
The solution to 5log_{b}(x)+2log_{b}(z) is log_{b}(x^5z^2)