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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{5} (3 x + 2) - lo g_{5} (x)

(lo g_{a} (x) - lo g_{a} (y)) + 8 lo g_{a} (v)

lo g_{10} (\frac{64}{z})

\frac{1}{3} lo g_{4} (x) + lo g_{4} (y) - 2

2 lo g_{10} (2 x)

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