What is 2ln(x)+7ln(y)-3ln(z) ?

The solution to 2ln(x)+7ln(y)-3ln(z) is ln((x^2y^7)/(z^3))

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simplify 2ln(x)+7ln(y)-3ln(z)

simplify

2 ln (x) + 7 ln (y) - 3 ln (z)

ln (\frac{x ^{2} y ^{7}}{z ^{3}})

Solution steps

2 ln (x) + 7 ln (y) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{2}) + 7 ln (y) - 3 ln (z)

Apply log rule:

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

7 ln (y) = ln (y^{7})

= ln (x^{2}) + ln (y^{7}) - 3 ln (z)

Apply log rule:

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

ln (x^{2}) + ln (y^{7}) = ln (x^{2} y^{7})

= ln (x^{2} y^{7}) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{2} y^{7}) - ln (z^{3})

Apply log rule:

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

ln (x^{2} y^{7}) - ln (z^{3}) = ln (\frac{x ^{2} y ^{7}}{z ^{3}})

= ln (\frac{x ^{2} y ^{7}}{z ^{3}})

ln (3) + 2 ln (x)

lo g_{9} (4) - lo g_{9} (7)

lo g_{2} (\frac{2 a ^{3}}{b})

\frac{1}{2} lo g_{a} (8 x^{2}) - \frac{1}{6} lo g_{a} (8 x^{3})

lo g_{3} (\frac{2 x}{y})

What is 2ln(x)+7ln(y)-3ln(z) ?
The solution to 2ln(x)+7ln(y)-3ln(z) is ln((x^2y^7)/(z^3))