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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (8) = 3 ln (2)

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

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

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

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

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

4 ln (x) - \frac{1}{5} ln (x^{4})

ln (v y) - ln (y) - 1

ln (40) - ln (60)