What is 5log_{b}(x)+6log_{b}(z) ?

The solution to 5log_{b}(x)+6log_{b}(z) is log_{b}(x^5z^6)

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simplify 5log_{b}(x)+6log_{b}(z)

simplify

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

lo g_{b} (x^{5} z^{6})

Solution steps

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

Apply log rule:

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

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

= lo g_{b} (x^{5}) + lo g_{b} (z^{6})

Apply log rule:

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

lo g_{b} (x^{5}) + lo g_{b} (z^{6}) = lo g_{b} (x^{5} z^{6})

= lo g_{b} (x^{5} z^{6})

lo g_{10} (3) 2

lo g_{10} (\frac{10}{y})

lo g_{10} (\frac{1}{y})

ln (\frac{13}{9})

What is 5log_{b}(x)+6log_{b}(z) ?
The solution to 5log_{b}(x)+6log_{b}(z) is log_{b}(x^5z^6)