What is ln((8x^2)/(3y)) ?

The solution to ln((8x^2)/(3y)) is 3ln(2)+2ln(x)-ln(3)-ln(y)

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simplify ln((8x^2)/(3y))

simplify

ln (\frac{8 x ^{2}}{3 y})

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

Solution steps

ln (\frac{8 x ^{2}}{3 y})

Apply log rule:

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

ln (\frac{8 x ^{2}}{3 y}) = ln (8 x^{2}) - ln (3 y)

= ln (8 x^{2}) - ln (3 y)

Apply log rule:

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

ln (8 x^{2}) = ln (8) + ln (x^{2}), ln (3 y) = ln (3) + ln (y)

= ln (8) + 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)

= ln (8) + 2 ln (x) - (ln (3) + ln (y))

ln (8) = 3 ln (2)

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

- (ln (3) + ln (y)) : - ln (3) - ln (y)

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

ln (3^{x - 2} (3^{x} - 10))

ln (ux)

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

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

2 lo g_{6} (u) + 6 lo g_{6} (v)

What is ln((8x^2)/(3y)) ?
The solution to ln((8x^2)/(3y)) is 3ln(2)+2ln(x)-ln(3)-ln(y)