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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{10} (\frac{y ^{4}}{x ^{5} z})

\frac{1}{4} lo g_{10} (33) + \frac{1}{4} lo g_{10} (44)

lo g_{b} (8 k)

lo g_{10} (1000 x)

lo g_{3} (x^{2} - 1) - lo g_{3} (x + 1)

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