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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{3} (\frac{9 x ^{7}}{y ^{5}})

lo g_{3} (9 v)

lo g_{a} (a^{2} x) - lo g_{a} (x^{2} a)

- 3 (ln (3) - ln (2))

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