What is 5ln(x)+2ln(y)-3ln(z) ?

The solution to 5ln(x)+2ln(y)-3ln(z) is ln((x^5y^2)/(z^3))

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simplify 5ln(x)+2ln(y)-3ln(z)

simplify

5 ln (x) + 2 ln (y) - 3 ln (z)

ln (\frac{x ^{5} y ^{2}}{z ^{3}})

Solution steps

5 ln (x) + 2 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}) + 2 ln (y) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{5}) + ln (y^{2}) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{5} y^{2}) - 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^{2}) - ln (z^{3})

Apply log rule:

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

ln (x^{5} y^{2}) - ln (z^{3}) = ln (\frac{x ^{5} y ^{2}}{z ^{3}})

= ln (\frac{x ^{5} y ^{2}}{z ^{3}})

lo g_{10} (\frac{y}{z ^{5}})

lo g_{10} (\frac{4 x}{3})

lo g_{6} (x^{2} - 36) - lo g_{6} (x - 6)

lo g_{6} (\frac{x ^{6} z}{y ^{6}})

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

What is 5ln(x)+2ln(y)-3ln(z) ?
The solution to 5ln(x)+2ln(y)-3ln(z) is ln((x^5y^2)/(z^3))