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

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

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

simplify

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

ln (5) + 2 ln (y) + ln (x) - 3 ln (z)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (5 y^{2} x) = ln (5) + ln (y^{2}) + ln (x)

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

Apply log rule:

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

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

= ln (5) + 2 ln (y) + ln (x) - 3 ln (z)

lo g_{7} (\frac{1}{7} a^{3} b)

lo g_{10} (\frac{z ^{3} x ^{4}}{y})

lo g_{10} (x^{6}) - lo g_{10} (x^{5})

lo g_{10} (24) - lo g_{10} (3) + lo g_{10} (16)

lo g_{2} (9) - lo g_{2} (11)

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