What is expand log_{4}((7x^2)/(y^3)) ?

The solution to expand log_{4}((7x^2)/(y^3)) is log_{4}(7)+2log_{4}(x)-3log_{4}(y)

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expand log_{4}((7x^2)/(y^3))

expand

lo g_{4} (\frac{7 x ^{2}}{y ^{3}})

lo g_{4} (7) + 2 lo g_{4} (x) - 3 lo g_{4} (y)

Solution steps

lo g_{4} (\frac{7 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{7 x ^{2}}{y ^{3}}) = lo g_{4} (7 x^{2}) - lo g_{4} (y^{3})

= lo g_{4} (7 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} (7 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} (7 x^{2}) = lo g_{4} (7) + lo g_{4} (x^{2})

= lo g_{4} (7) + 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} (7) + 2 lo g_{4} (x) - 3 lo g_{4} (y)

\frac{1}{3} (ln (x) - 3 ln (y + 1) + ln (x + 1))

- \frac{ln ( 2 ) ln ( - 1 )}{2 π}

3 ln ∣ x - 2 ∣ - ln ∣ x + 3 ∣

- lo g_{10} (7.2 \cdot 1 0^{-} 14)

50 (\frac{1}{25} ln ∣ x ∣ - \frac{1}{25} ln ∣ x + 25 ∣)^{'}

What is expand log_{4}((7x^2)/(y^3)) ?
The solution to expand log_{4}((7x^2)/(y^3)) is log_{4}(7)+2log_{4}(x)-3log_{4}(y)