What is 4ln(x)+5ln(y)-2ln(z) ?

The solution to 4ln(x)+5ln(y)-2ln(z) is ln((x^4y^5)/(z^2))

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simplify 4ln(x)+5ln(y)-2ln(z)

simplify

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

ln (\frac{x ^{4} y ^{5}}{z ^{2}})

Solution steps

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

Apply log rule:

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

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

= ln (x^{4}) + 5 ln (y) - 2 ln (z)

Apply log rule:

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

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

= ln (x^{4}) + ln (y^{5}) - 2 ln (z)

Apply log rule:

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

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

= ln (x^{4} y^{5}) - 2 ln (z)

Apply log rule:

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

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

= ln (x^{4} y^{5}) - ln (z^{2})

Apply log rule:

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

ln (x^{4} y^{5}) - ln (z^{2}) = ln (\frac{x ^{4} y ^{5}}{z ^{2}})

= ln (\frac{x ^{4} y ^{5}}{z ^{2}})

ln (\frac{9}{8 x ^{8} y})

lo g_{8} (7) - lo g_{8} (5)

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

What is 4ln(x)+5ln(y)-2ln(z) ?
The solution to 4ln(x)+5ln(y)-2ln(z) is ln((x^4y^5)/(z^2))