What is ln(8/(5x^5y)) ?

The solution to ln(8/(5x^5y)) is 3ln(2)-ln(5)-5ln(x)-ln(y)

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simplify ln(8/(5x^5y))

simplify

ln (\frac{8}{5 x ^{5} y})

3 ln (2) - ln (5) - 5 ln (x) - ln (y)

Solution steps

ln (\frac{8}{5 x ^{5} y})

Apply log rule:

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

ln (\frac{8}{5 x ^{5} y}) = ln (8) - ln (5 x^{5} y)

= ln (8) - ln (5 x^{5} y)

Apply log rule:

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

ln (5 x^{5} y) = ln (5) + ln (x^{5}) + ln (y)

= ln (8) - (ln (x^{5}) + ln (y) + ln (5))

Apply log rule:

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

ln (x^{5}) = 5 ln (x)

= ln (8) - (ln (5) + 5 ln (x) + ln (y))

ln (8) = 3 ln (2)

= 3 ln (2) - (5 ln (x) + ln (y) + ln (5))

- (ln (5) + 5 ln (x) + ln (y)) : - ln (5) - 5 ln (x) - ln (y)

= 3 ln (2) - ln (5) - 5 ln (x) - ln (y)

lo g_{3} (\frac{6 y}{z})

ln (\frac{e ^{6}}{7})

\frac{1}{3} lo g_{b} (x^{4} y^{5}) - \frac{3}{4} lo g_{b} (x^{2} y)

ln (\frac{89}{2})

lo g_{5} (\frac{125 b ^{5} y ^{2} - 8}{y ( x + 8 ) ^{2}})

What is ln(8/(5x^5y)) ?
The solution to ln(8/(5x^5y)) is 3ln(2)-ln(5)-5ln(x)-ln(y)