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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (x y^{4}) = ln (x) + ln (y^{4})

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

Apply log rule:

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

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

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

- lo g_{10} (1.5 \cdot 1 0^{- 7})

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

ln (\frac{8}{3.1 4 ^{2}} \cdot \frac{( 230 - 50 )}{( 65 - 50 )})

9.28 + lo g_{10} (\frac{0.15}{0.3})

lo g_{6} (x^{6}) - lo g_{6} (2 x^{2}) - lo g_{6} (x^{3})

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