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

The solution to 2ln(x)-3ln(y)-4ln(z) is ln((x^2)/(y^3z^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} (\frac{a}{b})

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

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

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

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

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

lo g_{3}^{2} (x + 2) - lo g_{3} (x^{2} + 4 x + 4)

lo g_{10} (27) - lo g_{10} (9)

2 lo g_{10} (3) - 3 lo g_{10} (2)

ln (5) + ln (2)

1 - lo g_{4} (m - 1) - lo g_{4} (m + 1)

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