What is ln(11)+3ln(x)-9ln(y) ?

The solution to ln(11)+3ln(x)-9ln(y) is ln((11x^3)/(y^9))

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simplify ln(11)+3ln(x)-9ln(y)

simplify

ln (11) + 3 ln (x) - 9 ln (y)

ln (\frac{11 x ^{3}}{y ^{9}})

Solution steps

ln (11) + 3 ln (x) - 9 ln (y)

Apply log rule:

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

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

= ln (11) + ln (x^{3}) - 9 ln (y)

Apply log rule:

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

ln (11) + ln (x^{3}) = ln (11 x^{3})

= ln (11 x^{3}) - 9 ln (y)

Apply log rule:

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

9 ln (y) = ln (y^{9})

= ln (11 x^{3}) - ln (y^{9})

Apply log rule:

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

ln (11 x^{3}) - ln (y^{9}) = ln (\frac{11 x ^{3}}{y ^{9}})

= ln (\frac{11 x ^{3}}{y ^{9}})

lo g_{3} (5) - lo g_{3} (8)

lo g_{4} (\frac{16}{x ^{4}})

lo g_{b} (x^{2} + 1) - \frac{1}{2} lo g_{b} (x^{2} + 2)

- (\frac{6}{7}) lo g_{2} (\frac{6}{7}) - (\frac{1}{7}) lo g_{2} (\frac{1}{7})

- lo g_{10} (3.2 \times 1 0^{- 4})

What is ln(11)+3ln(x)-9ln(y) ?
The solution to ln(11)+3ln(x)-9ln(y) is ln((11x^3)/(y^9))