What is ln(3)+4ln(x)-4ln(y) ?

The solution to ln(3)+4ln(x)-4ln(y) is ln((3x^4)/(y^4))

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simplify ln(3)+4ln(x)-4ln(y)

simplify

ln (3) + 4 ln (x) - 4 ln (y)

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

Solution steps

ln (3) + 4 ln (x) - 4 ln (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (3) + ln (x^{4}) - 4 ln (y)

Apply log rule:

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

ln (3) + ln (x^{4}) = ln (3 x^{4})

= ln (3 x^{4}) - 4 ln (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (3 x^{4}) - ln (y^{4})

Apply log rule:

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

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

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

lo g_{2} (\frac{5 x}{y})

x^{2} - 2 ln (8 x)

lo g_{4} (16 (x^{2} - 4))

lo g_{3} (\frac{1}{9} m n^{2})

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

What is ln(3)+4ln(x)-4ln(y) ?
The solution to ln(3)+4ln(x)-4ln(y) is ln((3x^4)/(y^4))