What is expand ln((3y)/(x^5)) ?

The solution to expand ln((3y)/(x^5)) is ln(3)+ln(y)-5ln(x)

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expand ln((3y)/(x^5))

expand

ln (\frac{3 y}{x ^{5}})

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

Solution steps

ln (\frac{3 y}{x ^{5}})

Apply log rule:

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

ln (\frac{3 y}{x ^{5}}) = ln (3 y) - ln (x^{5})

= ln (3 y) - ln (x^{5})

Apply log rule:

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

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

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

Apply log rule:

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

ln (3 y) = ln (3) + ln (y)

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

ln (x^{2} - 25) - ln (x + 5)

lo g_{10} (\frac{1}{20})

10 \cdot lo g_{10} (\frac{2 \cdot 1 0 ^{- 2}}{1 0 ^{- 12}})

ln (\frac{4}{13})

lo g_{7} (\frac{14}{49}) - ln (2)

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