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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{10} (\frac{4 x ^{3}}{y ^{2}})

lo g_{3} (20) - lo g_{3} (4)

ln (\frac{11}{16})

ln (\frac{3}{4}) - 1

ln (e^{3} \cdot (e^{2} - 1))

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