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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (\frac{x + 2}{x - 3})

4 ln (2) - \frac{1}{2} ln (25)

10 lo g_{10} (\frac{S}{1 0 ^{- 12}})

ln (\frac{67}{150})

lo g_{4} (\frac{c}{64})

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