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

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

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simplify-3log_{2}(x)-2log_{2}(y)

simplify

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

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

Solution steps

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

Apply log rule:

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

3 lo g_{2} (x) = lo g_{2} (x^{3})

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

Apply log rule:

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

2 lo g_{2} (y) = lo g_{2} (y^{2})

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

Rewrite

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

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

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

Apply log rule:

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

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

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

ln (\frac{1}{2}) + ln (1)

ln (\frac{1}{298})

ln (\frac{968.3}{896.5})

\frac{1}{3} lo g_{10} (245)

6 lo g_{b} (m) - 5 lo g_{b} (n) + 3

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