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

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

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simplify ln((x^2y^3)/(z^4))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

ln (\frac{760}{120})

360 ln (\frac{360.108}{360})

ln (\frac{x ^{4}}{y ^{2} z ^{5}})

\frac{ln ( 330 ) - ln ( 166 )}{7}

- lo g_{10} (3.4 x 1 0^{- 4})

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