What is 3ln(x)+5ln(y)-6ln(z) ?

The solution to 3ln(x)+5ln(y)-6ln(z) is ln((x^3y^5)/(z^6))

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simplify 3ln(x)+5ln(y)-6ln(z)

simplify

3 ln (x) + 5 ln (y) - 6 ln (z)

ln (\frac{x ^{3} y ^{5}}{z ^{6}})

Solution steps

3 ln (x) + 5 ln (y) - 6 ln (z)

Apply log rule:

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

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

= ln (x^{3}) + 5 ln (y) - 6 ln (z)

Apply log rule:

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

5 ln (y) = ln (y^{5})

= ln (x^{3}) + ln (y^{5}) - 6 ln (z)

Apply log rule:

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

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

= ln (x^{3} y^{5}) - 6 ln (z)

Apply log rule:

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

6 ln (z) = ln (z^{6})

= ln (x^{3} y^{5}) - ln (z^{6})

Apply log rule:

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

ln (x^{3} y^{5}) - ln (z^{6}) = ln (\frac{x ^{3} y ^{5}}{z ^{6}})

= ln (\frac{x ^{3} y ^{5}}{z ^{6}})

lo g_{3} (4) + 2 lo g_{3} (5)

6 lo g_{10} (x) + lo g_{10} (y) - lo g_{10} (z)

ln (y) - ln (x)

lo g_{10} (a) - lo g_{10} (b) - lo g_{10} (c)

lo g_{3} (5) + lo g_{3} (2)

What is 3ln(x)+5ln(y)-6ln(z) ?
The solution to 3ln(x)+5ln(y)-6ln(z) is ln((x^3y^5)/(z^6))