What is 4log_{b}(y)+8log_{b}(z) ?

The solution to 4log_{b}(y)+8log_{b}(z) is log_{b}(y^4z^8)

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simplify 4log_{b}(y)+8log_{b}(z)

simplify

4 lo g_{b} (y) + 8 lo g_{b} (z)

lo g_{b} (y^{4} z^{8})

Solution steps

4 lo g_{b} (y) + 8 lo g_{b} (z)

Apply log rule:

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

4 lo g_{b} (y) = lo g_{b} (y^{4})

= lo g_{b} (y^{4}) + 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} (y^{4}) + lo g_{b} (z^{8})

Apply log rule:

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

lo g_{b} (y^{4}) + lo g_{b} (z^{8}) = lo g_{b} (y^{4} z^{8})

= lo g_{b} (y^{4} z^{8})

lo g_{b} (\frac{5 x + 1}{3 x - 2})

lo g_{2} (8) - lo g_{10} (2 x) - lo g_{10} (2 y)

ln (\frac{e ^{8}}{3})

4 ln (x) - 5 ln (y) - 6 ln (z)

- (\frac{3}{5} lo g_{2} (\frac{3}{5}) + \frac{2}{5} lo g_{2} (\frac{2}{5}))

What is 4log_{b}(y)+8log_{b}(z) ?
The solution to 4log_{b}(y)+8log_{b}(z) is log_{b}(y^4z^8)