What is log_{2}(9)-log_{2}(y)+1/2 log_{2}(x) ?

The solution to log_{2}(9)-log_{2}(y)+1/2 log_{2}(x) is log_{2}((9sqrt(x))/y)

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simplify log_{2}(9)-log_{2}(y)+1/2 log_{2}(x)

simplify

lo g_{2} (9) - lo g_{2} (y) + \frac{1}{2} lo g_{2} (x)

lo g_{2} (\frac{9 x}{y})

Solution steps

lo g_{2} (9) - lo g_{2} (y) + \frac{1}{2} lo g_{2} (x)

Apply log rule:

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

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

= lo g_{2} (9) - lo g_{2} (y) + lo g_{2} (x^{\frac{1}{2}})

Apply log rule:

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

lo g_{2} (9) - lo g_{2} (y) = lo g_{2} (\frac{9}{y})

= lo g_{2} (\frac{9}{y}) + lo g_{2} (x^{\frac{1}{2}})

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{2} (\frac{9}{y}) + lo g_{2} (x^{\frac{1}{2}}) = lo g_{2} (\frac{9}{y} x^{\frac{1}{2}})

= lo g_{2} (\frac{9}{y} x^{\frac{1}{2}})

Simplify

\frac{9}{y} x^{\frac{1}{2}} : \frac{9 x ^{\frac{1}{2}}}{y}

= lo g_{2} (\frac{9 x ^{\frac{1}{2}}}{y})

Apply exponent rule:

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

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

= lo g_{2} (\frac{9 x}{y})

\frac{1}{18} ln (\frac{167}{23})

lo g_{10} (A) + lo g_{10} (B) - lo g_{10} (\frac{1}{C})

lo g_{7} (\frac{49 m ^{6}}{k ^{3}})

3.79588 + lo g_{10} (\frac{0.2}{0.5})

lo g_{10} (2 c d)

What is log_{2}(9)-log_{2}(y)+1/2 log_{2}(x) ?
The solution to log_{2}(9)-log_{2}(y)+1/2 log_{2}(x) is log_{2}((9sqrt(x))/y)