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

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

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

simplify

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

lo g_{2} (3)

Decimal Notation

1.58496 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{x ^{4} \cdot 3}{( x ^{2} ) ^{2}} = 3

= lo g_{2} (3)

lo g_{3} (x^{5} y^{3})

ln (\frac{134.8}{15})

- ln (x y^{2})

\frac{1}{4} lo g_{10} (2)

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

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