What is 2ln(x)+3ln(y)-4ln(z) ?

The solution to 2ln(x)+3ln(y)-4ln(z) is ln((x^2y^3)/(z^4))

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simplify 2ln(x)+3ln(y)-4ln(z)

simplify

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

ln (\frac{x ^{2} y ^{3}}{z ^{4}})

Solution steps

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

Apply log rule:

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

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

= ln (x^{2}) + 3 ln (y) - 4 ln (z)

Apply log rule:

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

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

= ln (x^{2}) + ln (y^{3}) - 4 ln (z)

Apply log rule:

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

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

= ln (x^{2} y^{3}) - 4 ln (z)

Apply log rule:

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

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

= ln (x^{2} y^{3}) - ln (z^{4})

Apply log rule:

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

ln (x^{2} y^{3}) - ln (z^{4}) = ln (\frac{x ^{2} y ^{3}}{z ^{4}})

= ln (\frac{x ^{2} y ^{3}}{z ^{4}})

\frac{9 ln ( 5 )}{2 ln ( 3 ) - ln ( 5 )}

lo g_{10} (3 x + 10) - lo g_{10} (x)

lo g_{10} (a) + 4 lo g_{10} (b)

- (\frac{3}{7}) lo g_{2} (\frac{3}{7}) - (\frac{4}{7}) lo g_{2} (\frac{4}{7})

2 ln (2) - ln (5)

What is 2ln(x)+3ln(y)-4ln(z) ?
The solution to 2ln(x)+3ln(y)-4ln(z) is ln((x^2y^3)/(z^4))