What is simplify-2log_{b}(x)-3log_{b}(y)+log_{b}(z) ?

The solution to simplify-2log_{b}(x)-3log_{b}(y)+log_{b}(z) is log_{b}(z/(x^2y^3))

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simplify-2log_{b}(x)-3log_{b}(y)+log_{b}(z)

simplify

- 2 lo g_{b} (x) - 3 lo g_{b} (y) + lo g_{b} (z)

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

Solution steps

- 2 lo g_{b} (x) - 3 lo g_{b} (y) + lo g_{b} (z)

Apply log rule:

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

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

= - lo g_{b} (x^{2}) - 3 lo g_{b} (y) + lo g_{b} (z)

Apply log rule:

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

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

= - lo g_{b} (x^{2}) - lo g_{b} (y^{3}) + lo g_{b} (z)

Rewrite

- lo g_{b} (x^{2}) - lo g_{b} (y^{3})

- (lo g_{b} (x^{2}) + lo g_{b} (y^{3}))

= - (lo g_{b} (x^{2}) + lo g_{b} (y^{3})) + lo g_{b} (z)

Apply log rule:

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

lo g_{b} (x^{2}) + lo g_{b} (y^{3}) = lo g_{b} (x^{2} y^{3})

= - lo g_{b} (x^{2} y^{3}) + lo g_{b} (z)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{b} (z) - lo g_{b} (x^{2} y^{3}) = lo g_{b} (\frac{z}{x ^{2} y ^{3}})

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

lo g_{2} (5 \cdot 6 \cdot 3)

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

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

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

What is simplify-2log_{b}(x)-3log_{b}(y)+log_{b}(z) ?
The solution to simplify-2log_{b}(x)-3log_{b}(y)+log_{b}(z) is log_{b}(z/(x^2y^3))