What is ln((12x^4)/(y^2)) ?

The solution to ln((12x^4)/(y^2)) is ln(12)+4ln(x)-2ln(y)

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simplify ln((12x^4)/(y^2))

simplify

ln (\frac{12 x ^{4}}{y ^{2}})

ln (12) + 4 ln (x) - 2 ln (y)

Solution steps

ln (\frac{12 x ^{4}}{y ^{2}})

Apply log rule:

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

ln (\frac{12 x ^{4}}{y ^{2}}) = ln (12 x^{4}) - ln (y^{2})

= ln (12 x^{4}) - ln (y^{2})

Apply log rule:

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

ln (y^{2}) = 2 ln (y)

= ln (12 x^{4}) - 2 ln (y)

Apply log rule:

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

ln (12 x^{4}) = ln (12) + ln (x^{4})

= ln (12) + ln (x^{4}) - 2 ln (y)

Apply log rule:

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

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

= ln (12) + 4 ln (x) - 2 ln (y)

ln (\frac{sin ( ka )}{ka})

ln (19 e)

lo g_{6} (\frac{x - 4}{x ^{4}})

What is ln((12x^4)/(y^2)) ?
The solution to ln((12x^4)/(y^2)) is ln(12)+4ln(x)-2ln(y)