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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2 lo g_{3} (x) + lo g_{3} (y) - \frac{1}{2} lo g_{3} (z)

ln (a b^{t}) - ln ((ab)^{t}) - 2 ln (a)

ln (\frac{7}{6})

lo g_{10} (0.01) - lo g_{10} (0.001)

lo g_{10} (\frac{y}{4 y + 8})

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