What is 5log_{b}(x)+8log_{b}(z) ?

The solution to 5log_{b}(x)+8log_{b}(z) is log_{b}(x^5z^8)

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simplify 5log_{b}(x)+8log_{b}(z)

simplify

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

lo g_{b} (x^{5} z^{8})

Solution steps

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

Apply log rule:

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

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

= lo g_{b} (x^{5}) + lo g_{b} (z^{8})

Apply log rule:

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

lo g_{b} (x^{5}) + lo g_{b} (z^{8}) = lo g_{b} (x^{5} z^{8})

= lo g_{b} (x^{5} z^{8})

ln (3 (1))

ln (\frac{e ^{7}}{5})

lo g_{w} (\frac{13 x}{2})

ln (\frac{3 a ^{3} a ^{2}}{a})

lo g_{10} (\frac{x}{100 y ^{6}})

What is 5log_{b}(x)+8log_{b}(z) ?
The solution to 5log_{b}(x)+8log_{b}(z) is log_{b}(x^5z^8)