What is 3log_{2}(x)-4log_{2}(x+3)+log_{2}(y) ?

The solution to 3log_{2}(x)-4log_{2}(x+3)+log_{2}(y) is log_{2}((x^3y)/((x+3)^4))

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simplify 3log_{2}(x)-4log_{2}(x+3)+log_{2}(y)

simplify

3 lo g_{2} (x) - 4 lo g_{2} (x + 3) + lo g_{2} (y)

lo g_{2} (\frac{x ^{3} y}{( x + 3 ) ^{4}})

Solution steps

3 lo g_{2} (x) - 4 lo g_{2} (x + 3) + 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}) - 4 lo g_{2} (x + 3) + lo g_{2} (y)

Apply log rule:

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

4 lo g_{2} (x + 3) = lo g_{2} ((x + 3)^{4})

= lo g_{2} (x^{3}) - lo g_{2} ((x + 3)^{4}) + lo g_{2} (y)

Apply log rule:

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

lo g_{2} (x^{3}) - lo g_{2} ((x + 3)^{4}) = lo g_{2} (\frac{x ^{3}}{( x + 3 ) ^{4}})

= lo g_{2} (\frac{x ^{3}}{( x + 3 ) ^{4}}) + lo g_{2} (y)

Apply log rule:

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

lo g_{2} (\frac{x ^{3}}{( x + 3 ) ^{4}}) + lo g_{2} (y) = lo g_{2} (\frac{x ^{3}}{( x + 3 ) ^{4}} y)

= lo g_{2} (\frac{x ^{3}}{( x + 3 ) ^{4}} y)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= lo g_{2} (\frac{x ^{3} y}{( x + 3 ) ^{4}})

lo g_{a} (x \cdot y)

ln (7) - ln (14)

4 lo g_{10} (2) + lo g_{10} (3)

lo g_{b} (4 x^{2} y)

- lo g_{10} (3 \cdot 1 0^{- 8})

What is 3log_{2}(x)-4log_{2}(x+3)+log_{2}(y) ?
The solution to 3log_{2}(x)-4log_{2}(x+3)+log_{2}(y) is log_{2}((x^3y)/((x+3)^4))