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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (8) = 3 ln (2)

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

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

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

lo g_{\frac{1}{2}} (\frac{7}{12})

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

lo g_{5} (3) + lo g_{5} (r) - lo g_{5} (w)

7 ln (x) - \frac{1}{7} ln (y)

lo g_{b} (\frac{x ^{3} y}{z ^{8}})

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