What is 5ln(x)+4ln(y)-3ln(z) ?

The solution to 5ln(x)+4ln(y)-3ln(z) is ln((x^5y^4)/(z^3))

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simplify 5ln(x)+4ln(y)-3ln(z)

simplify

5 ln (x) + 4 ln (y) - 3 ln (z)

ln (\frac{x ^{5} y ^{4}}{z ^{3}})

Solution steps

5 ln (x) + 4 ln (y) - 3 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) - 3 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}) - 3 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}) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{5} y^{4}) - ln (z^{3})

Apply log rule:

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

ln (x^{5} y^{4}) - ln (z^{3}) = ln (\frac{x ^{5} y ^{4}}{z ^{3}})

= ln (\frac{x ^{5} y ^{4}}{z ^{3}})

lo g_{6} ((\frac{x}{216})^{4})

\frac{ln ( 2.5 ) - ln ( 2.2 )}{2.5 - 2.2}

ln (3) - 2 ln (2)

What is 5ln(x)+4ln(y)-3ln(z) ?
The solution to 5ln(x)+4ln(y)-3ln(z) is ln((x^5y^4)/(z^3))