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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (2 x) = ln (2) + ln (x)

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

ln (2) + ln (x + 1) - \frac{ln ( 4 x + 7 )}{3}

lo g_{6} (\frac{36 - 4}{21 6 ^{3}})

lo g_{8} ((\frac{x ^{3} y}{z})^{2})

- ln (57) + ln (123)

lo g_{e} (3 x + 1) + lo g_{e} (2)

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