What is ln((2x^3sqrt(y^3-1))/(z^5)) ?

The solution to ln((2x^3sqrt(y^3-1))/(z^5)) is ln(2)+3ln(x)+ln(sqrt(y^3-1))-5ln(z)

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simplify ln((2x^3sqrt(y^3-1))/(z^5))

simplify

ln (\frac{2 x ^{3} y ^{3} - 1}{z ^{5}})

ln (2) + 3 ln (x) + ln (y^{3} - 1) - 5 ln (z)

Solution steps

ln (\frac{2 x ^{3} y ^{3} - 1}{z ^{5}})

Apply log rule:

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

ln (\frac{2 x ^{3} y ^{3} - 1}{z ^{5}}) = ln (2 x^{3} y^{3} - 1) - ln (z^{5})

= ln (2 x^{3} y^{3} - 1) - ln (z^{5})

Apply log rule:

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

ln (z^{5}) = 5 ln (z)

= ln (2 x^{3} y^{3} - 1) - 5 ln (z)

Apply log rule:

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

ln (2 x^{3} y^{3} - 1) = ln (2) + ln (x^{3}) + ln (y^{3} - 1)

= ln (2) + ln (x^{3}) + ln (y^{3} - 1) - 5 ln (z)

Apply log rule:

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

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

= ln (2) + 3 ln (x) + ln (y^{3} - 1) - 5 ln (z)

lo g_{6} (\frac{16 x ^{2}}{2 x - 4})

lo g_{7} (\frac{x ^{4}}{y ^{2}})

lo g_{2} (\frac{4}{x + 9})

lo g_{10} (y) + 2 lo g_{10} (z)

lo g_{10} (\frac{x ^{33} y ^{20}}{z ^{36}})

What is ln((2x^3sqrt(y^3-1))/(z^5)) ?
The solution to ln((2x^3sqrt(y^3-1))/(z^5)) is ln(2)+3ln(x)+ln(sqrt(y^3-1))-5ln(z)