What is log_{2}(sqrt(6))-1/2 log_{2}(3) ?

The solution to log_{2}(sqrt(6))-1/2 log_{2}(3) is 1/2

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simplify log_{2}(sqrt(6))-1/2 log_{2}(3)

simplify

lo g_{2} (6) - \frac{1}{2} lo g_{2} (3)

\frac{1}{2}

Decimal Notation

0.5

Solution steps

lo g_{2} (6) - \frac{1}{2} lo g_{2} (3)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

- \frac{1}{2} lo g_{2} (3) = - lo g_{2} (3^{\frac{1}{2}})

= lo g_{2} (6) - lo g_{2} (3^{\frac{1}{2}})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{2} (6) - lo g_{2} (3^{\frac{1}{2}}) = lo g_{2} (\frac{6}{3 ^{\frac{1}{2}}})

= lo g_{2} (\frac{6}{3 ^{\frac{1}{2}}})

Cancel

\frac{6}{3 ^{\frac{1}{2}}} : 2

= lo g_{2} (2)

Apply radical rule:

a = a^{\frac{1}{2}}

2 = 2^{\frac{1}{2}}

= lo g_{2} (2^{\frac{1}{2}})

Apply log rule:

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

= \frac{1}{2}

5 ln (x^{3}) - \frac{1}{3} ln (7 - x^{3})

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

lo g_{3} (\frac{27}{x + 3})

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

ln (35 a) - ln (7)

What is log_{2}(sqrt(6))-1/2 log_{2}(3) ?
The solution to log_{2}(sqrt(6))-1/2 log_{2}(3) is 1/2