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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- (3 ln (x) + 2 ln (z)) : - 3 ln (x) - 2 ln (z)

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

ln (\frac{y ^{'} ( t )}{5})

sin (arctan (x))

sin (arccos (x))

cos (arcsin (x))

sin (- x)

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