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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2 ln (3) + 3 ln (2)

ln (\frac{1}{2}) - ln (\frac{3}{2})

lo g_{2} (\frac{y}{a})

ln (6) + ln (4)

lo g_{7} (\frac{y}{343})

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