What is ln(5)+3ln(x)-2ln(y) ?

The solution to ln(5)+3ln(x)-2ln(y) is ln((5x^3)/(y^2))

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simplify ln(5)+3ln(x)-2ln(y)

simplify

ln (5) + 3 ln (x) - 2 ln (y)

ln (\frac{5 x ^{3}}{y ^{2}})

Solution steps

ln (5) + 3 ln (x) - 2 ln (y)

Apply log rule:

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

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

= ln (5) + ln (x^{3}) - 2 ln (y)

Apply log rule:

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

ln (5) + ln (x^{3}) = ln (5 x^{3})

= ln (5 x^{3}) - 2 ln (y)

Apply log rule:

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

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

= ln (5 x^{3}) - ln (y^{2})

Apply log rule:

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

ln (5 x^{3}) - ln (y^{2}) = ln (\frac{5 x ^{3}}{y ^{2}})

= ln (\frac{5 x ^{3}}{y ^{2}})

- 2 ln (\frac{2}{3})

ln (\frac{10}{11})

lo g_{10} (\frac{y ^{5} x ^{2}}{z ^{5}})

lo g_{x} (\frac{1}{32})

ln (2 n) - ln (n + 2)

What is ln(5)+3ln(x)-2ln(y) ?
The solution to ln(5)+3ln(x)-2ln(y) is ln((5x^3)/(y^2))