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

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

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

simplify

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

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

Solution steps

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

lo g_{10} (a) + 2 lo g_{10} (b) - 3 lo g_{10} (c)

ln ((\frac{1}{x})^{\frac{1}{l n ( x )}})

ln (\frac{486}{271})

\frac{4 ln ( 2 )}{ln ( \frac{512}{3} )}

ln (\frac{400}{100})

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