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

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

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

simplify

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

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

Solution steps

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

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)

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})

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}})

ln (0.8) - ln (0.74)

\frac{1}{10} ln (\frac{0.267 - 0.017}{0.132 - 0.017})

4 lo g_{c} (y) - \frac{14}{3} lo g_{c} (x)

ln (130) - ln (5)

\frac{1}{3} lo g_{8} (7)

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