What is 2ln(x)-3ln(z)-ln(w) ?

The solution to 2ln(x)-3ln(z)-ln(w) is ln((x^2)/(z^3w))

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simplify 2ln(x)-3ln(z)-ln(w)

simplify

2 ln (x) - 3 ln (z) - ln (w)

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

Solution steps

2 ln (x) - 3 ln (z) - ln (w)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply the fraction rule:

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

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

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

ln (3 x) - ln (5 y)

38 ln (\frac{90}{10})

ln (a e^{b t})

ln (\frac{2 - x}{x + 1})

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