What is ln(4/(5x^5y)) ?

The solution to ln(4/(5x^5y)) is 2ln(2)-ln(5)-5ln(x)-ln(y)

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simplify ln(4/(5x^5y))

simplify

ln (\frac{4}{5 x ^{5} y})

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

Solution steps

ln (\frac{4}{5 x ^{5} y})

Apply log rule:

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

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

= ln (4) - 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 (4) - (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 (4) - (ln (5) + 5 ln (x) + ln (y))

ln (4) = 2 ln (2)

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

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

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

lo g_{5} (x) + \frac{1}{3} lo g_{5} (y) - 4 lo g_{5} (z)

lo g_{10} (3 y (5 y + 8))

lo g_{10} (\frac{x}{y ^{6}})

4 lo g_{10} (x) - lo g_{10} (x + 11)

lo g_{10} (\frac{x y ^{4}}{z ^{3}})

What is ln(4/(5x^5y)) ?
The solution to ln(4/(5x^5y)) is 2ln(2)-ln(5)-5ln(x)-ln(y)