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

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

Popular >

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2 ln (4) + 5 ln (x) + 3 ln (y)

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

2000 (ln (140000) - ln (77000)) - 294

\frac{1}{2} ln (2 x) + \frac{5}{4} ln (4 x - 4) - \frac{3}{4} ln (4 x - 4)

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

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