What is expand log_{4}((3x^2)/(y^3)) ?

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

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expand log_{4}((3x^2)/(y^3))

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{4} (y^{3}) = 3 lo g_{4} (y)

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (\frac{( x y ^{4} )}{z ^{3}})

- lo g_{10} (1.5 \cdot 1 0^{- 7})

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

ln (\frac{8}{3.1 4 ^{2}} \cdot \frac{( 230 - 50 )}{( 65 - 50 )})

9.28 + lo g_{10} (\frac{0.15}{0.3})

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