What is 2ln(x)+5ln(y)-6ln(z) ?

The solution to 2ln(x)+5ln(y)-6ln(z) is ln((x^2y^5)/(z^6))

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simplify 2ln(x)+5ln(y)-6ln(z)

simplify

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

ln (\frac{x ^{2} y ^{5}}{z ^{6}})

Solution steps

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

Apply log rule:

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

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

= ln (x^{2}) + 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^{2}) + ln (y^{5}) - 6 ln (z)

Apply log rule:

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

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

= ln (x^{2} 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^{2} y^{5}) - ln (z^{6})

Apply log rule:

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

ln (x^{2} y^{5}) - ln (z^{6}) = ln (\frac{x ^{2} y ^{5}}{z ^{6}})

= ln (\frac{x ^{2} y ^{5}}{z ^{6}})

x ln (2) + 5 ln (x - 1) - 2 ln (x + 3)

ln (\frac{243}{625})

ln (\frac{e ^{5}}{11})

\frac{1}{5} ln (2) + \frac{4}{5} ln (\frac{3}{4})

lo g_{3} (M) - lo g_{3} (N)

What is 2ln(x)+5ln(y)-6ln(z) ?
The solution to 2ln(x)+5ln(y)-6ln(z) is ln((x^2y^5)/(z^6))