What is ln((7x^3)/(y^2)) ?

The solution to ln((7x^3)/(y^2)) is ln(7)+3ln(x)-2ln(y)

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simplify ln((7x^3)/(y^2))

simplify

ln (\frac{7 x ^{3}}{y ^{2}})

ln (7) + 3 ln (x) - 2 ln (y)

Solution steps

ln (\frac{7 x ^{3}}{y ^{2}})

Apply log rule:

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

ln (\frac{7 x ^{3}}{y ^{2}}) = ln (7 x^{3}) - ln (y^{2})

= ln (7 x^{3}) - ln (y^{2})

Apply log rule:

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

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

= ln (7 x^{3}) - 2 ln (y)

Apply log rule:

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

ln (7 x^{3}) = ln (7) + ln (x^{3})

= ln (7) + ln (x^{3}) - 2 ln (y)

Apply log rule:

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

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

= ln (7) + 3 ln (x) - 2 ln (y)

lo g_{3} (\frac{5}{q ^{2} p})

ln (3 - x^{2}) - ln (x + 3)

ln (x^{2} - 13 x + 36) + 2 ln (x - 4) - ln (x - 9)

lo g_{b} (m^{3} n^{2} p^{5})

lo g_{8} (\frac{64}{x + 1})

What is ln((7x^3)/(y^2)) ?
The solution to ln((7x^3)/(y^2)) is ln(7)+3ln(x)-2ln(y)