What is 6ln(x)+5ln(y)-4ln(z) ?

The solution to 6ln(x)+5ln(y)-4ln(z) is ln((x^6y^5)/(z^4))

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simplify 6ln(x)+5ln(y)-4ln(z)

simplify

6 ln (x) + 5 ln (y) - 4 ln (z)

ln (\frac{x ^{6} y ^{5}}{z ^{4}})

Solution steps

6 ln (x) + 5 ln (y) - 4 ln (z)

Apply log rule:

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

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

= ln (x^{6}) + 5 ln (y) - 4 ln (z)

Apply log rule:

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

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

= ln (x^{6}) + ln (y^{5}) - 4 ln (z)

Apply log rule:

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

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

= ln (x^{6} y^{5}) - 4 ln (z)

Apply log rule:

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

4 ln (z) = ln (z^{4})

= ln (x^{6} y^{5}) - ln (z^{4})

Apply log rule:

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

ln (x^{6} y^{5}) - ln (z^{4}) = ln (\frac{x ^{6} y ^{5}}{z ^{4}})

= ln (\frac{x ^{6} y ^{5}}{z ^{4}})

lo g_{b} (x^{3})

lo g_{4} ((x^{5} y)^{5})

lo g_{7} (4) + lo g_{7} (3)

lo g_{2} (5) + lo g_{2} (11)

ln (e^{x} y)

What is 6ln(x)+5ln(y)-4ln(z) ?
The solution to 6ln(x)+5ln(y)-4ln(z) is ln((x^6y^5)/(z^4))