What is expand ln((2x^4)/(y^7)) ?

The solution to expand ln((2x^4)/(y^7)) is ln(2)+4ln(x)-7ln(y)

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expand ln((2x^4)/(y^7))

expand

ln (\frac{2 x ^{4}}{y ^{7}})

ln (2) + 4 ln (x) - 7 ln (y)

Solution steps

ln (\frac{2 x ^{4}}{y ^{7}})

Apply log rule:

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

ln (\frac{2 x ^{4}}{y ^{7}}) = ln (2 x^{4}) - ln (y^{7})

= ln (2 x^{4}) - ln (y^{7})

Apply log rule:

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

ln (y^{7}) = 7 ln (y)

= ln (2 x^{4}) - 7 ln (y)

Apply log rule:

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

ln (2 x^{4}) = ln (2) + ln (x^{4})

= ln (2) + ln (x^{4}) - 7 ln (y)

Apply log rule:

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

ln (x^{4}) = 4 ln (x)

= ln (2) + 4 ln (x) - 7 ln (y)

\frac{1}{2} ln ∣ 2 x + 1 ∣ + 2 ln ∣ x - 1 ∣ + C

\frac{π}{2} ln (3)

lo g_{10} (x) - 4 lo g_{10} (y)

ln (e^{x^{2}} cos (5 x - 7))

lo g_{3} (8) + lo g_{3} (x) - 2 lo g_{3} (x + 4)

What is expand ln((2x^4)/(y^7)) ?
The solution to expand ln((2x^4)/(y^7)) is ln(2)+4ln(x)-7ln(y)